calculus 2 series and sequences practice test

Absolute Convergence In this section we will have a brief discussion on absolute convergence and conditionally convergent and how they relate to convergence of infinite series. Don't all infinite series grow to infinity? /Length 1722 endstream 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 Ex 11.11.4 Show that \(\cos x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as N approaches infinity. OR sequences are lists of numbers, where the numbers may or may not be determined by a pattern. Our mission is to provide a free, world-class education to anyone, anywhere. 508.8 453.8 482.6 468.9 563.7 334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 If a geometric series begins with the following term, what would the next term be? Worked example: sequence convergence/divergence, Partial sums: formula for nth term from partial sum, Partial sums: term value from partial sum, Worked example: convergent geometric series, Worked example: divergent geometric series, Infinite geometric series word problem: bouncing ball, Infinite geometric series word problem: repeating decimal, Proof of infinite geometric series formula, Convergent & divergent geometric series (with manipulation), Level up on the above skills and collect up to 320 Mastery points, Determine absolute or conditional convergence, Level up on the above skills and collect up to 640 Mastery points, Worked example: alternating series remainder, Taylor & Maclaurin polynomials intro (part 1), Taylor & Maclaurin polynomials intro (part 2), Worked example: coefficient in Maclaurin polynomial, Worked example: coefficient in Taylor polynomial, Visualizing Taylor polynomial approximations, Worked example: estimating sin(0.4) using Lagrange error bound, Worked example: estimating e using Lagrange error bound, Worked example: cosine function from power series, Worked example: recognizing function from Taylor series, Maclaurin series of sin(x), cos(x), and e, Finding function from power series by integrating, Integrals & derivatives of functions with known power series, Interval of convergence for derivative and integral, Converting explicit series terms to summation notation, Converting explicit series terms to summation notation (n 2), Formal definition for limit of a sequence, Proving a sequence converges using the formal definition, Infinite geometric series formula intuition, Proof of infinite geometric series as a limit. Calculus II For Dummies Cheat Sheet - dummies 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6 944.4 472.2 833.3 (answer), Ex 11.1.4 Determine whether \(\left\{{n^2+1\over (n+1)^2}\right\}_{n=0}^{\infty}\) converges or diverges. /Length 200 Determine whether the sequence converges or diverges. PDF Ap Calculus Ab Bc Kelley Copy - gny.salvationarmy.org The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al. n a n converges if and only if the integral 1 f ( x) d x converges. Calculus (single and multi-variable) Ordinary Differential equations (upto 2nd order linear with Laplace transforms, including Dirac Delta functions and Fourier Series. You appear to be on a device with a "narrow" screen width (, 2.4 Equations With More Than One Variable, 2.9 Equations Reducible to Quadratic in Form, 4.1 Lines, Circles and Piecewise Functions, 1.5 Trig Equations with Calculators, Part I, 1.6 Trig Equations with Calculators, Part II, 3.6 Derivatives of Exponential and Logarithm Functions, 3.7 Derivatives of Inverse Trig Functions, 4.10 L'Hospital's Rule and Indeterminate Forms, 5.3 Substitution Rule for Indefinite Integrals, 5.8 Substitution Rule for Definite Integrals, 6.3 Volumes of Solids of Revolution / Method of Rings, 6.4 Volumes of Solids of Revolution/Method of Cylinders, A.2 Proof of Various Derivative Properties, A.4 Proofs of Derivative Applications Facts, 7.9 Comparison Test for Improper Integrals, 9. /FirstChar 0 (answer), Ex 11.1.5 Determine whether \(\left\{{n+47\over\sqrt{n^2+3n}}\right\}_{n=1}^{\infty}\) converges or diverges. << YesNo 2.(b). /Subtype/Type1 1 2 + 1 4 + 1 8 + = n=1 1 2n = 1 We will need to be careful, but it turns out that we can . Given that \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{n^3} + 1}}} = 1.6865\) determine the value of \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{{n^3} + 1}}} \). May 3rd, 2018 - Sequences and Series Practice Test Determine if the sequence is arithmetic Find the term named in the problem 27 4 8 16 Sequences and Series Practice for Test Mr C Miller April 30th, 2018 - Determine if the sequence is arithmetic or geometric the problem 3 Sequences and Series Practice for Test Series Algebra II Math Khan Academy At this time, I do not offer pdf's for solutions to individual problems. xYKs6W(MCG:9iIO=(lkFRI$x$AMN/" J?~i~d cXf9o/r.&Lxy%/D-Yt+"LX]Sfp]Xl-aM_[6(*~mQbh*28AjZx0 =||. ]^e-V!2 F. Ex 11.7.3 Compute \(\lim_{n\to\infty} |a_n|^{1/n}\) for the series \(\sum 1/n^2\). Then we can say that the series diverges without having to do any extra work. (answer), Ex 11.4.6 Approximate \(\sum_{n=1}^\infty (-1)^{n-1}{1\over n^4}\) to two decimal places. 0 Choose your answer to the question and click 'Continue' to see how you did. We will illustrate how we can find a series representation for indefinite integrals that cannot be evaluated by any other method. Learn how this is possible, how we can tell whether a series converges, and how we can explore convergence in . 8 0 obj (answer), Ex 11.3.10 Find an \(N\) so that \(\sum_{n=0}^\infty {1\over e^n}\) is between \(\sum_{n=0}^N {1\over e^n}\) and \(\sum_{n=0}^N {1\over e^n} + 10^{-4}\). Each term is the difference of the previous two terms. All other trademarks and copyrights are the property of their respective owners. (You may want to use Sage or a similar aid.) The Root Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. Which of the following sequences is NOT a geometric sequence? Determine whether the following series converge or diverge. /Subtype/Type1 Which of the following sequences is NOT a geometric sequence? >> Study Online AP Calculus AB and BC: Chapter 9 -Infinite Sequences and Series : 9.2 -The Integral Test and p-Series Study Notes Prepared by AP Teachers Skip to content . Applications of Series In this section we will take a quick look at a couple of applications of series. Martha_Austin Teacher. Legal. << /BaseFont/VMQJJE+CMR8 Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses. }\) (answer), Ex 11.8.3 \(\sum_{n=1}^\infty {n!\over n^n}x^n\) (answer), Ex 11.8.4 \(\sum_{n=1}^\infty {n!\over n^n}(x-2)^n\) (answer), Ex 11.8.5 \(\sum_{n=1}^\infty {(n! 531.3 531.3 531.3 295.1 295.1 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. If it converges, compute the limit. 979.2 979.2 979.2 272 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 Sequences and Series. /Length 1247 In order to use either test the terms of the infinite series must be positive. We will also give many of the basic facts, properties and ways we can use to manipulate a series. Math Journey: Calculus, ODEs, Linear Algebra and Beyond A ball is dropped from an unknown height (h) and it repeatedly bounces on the floor. Given that n=0 1 n3 +1 = 1.6865 n = 0 1 n 3 + 1 = 1.6865 determine the value of n=2 1 n3 +1 . << /Subtype/Type1 (answer). /Filter /FlateDecode Each term is the sum of the previous two terms. Section 10.3 : Series - Basics. SAT Practice Questions- All Maths; SAT Practice Test Questions- Reading , Writing and Language; KS 1-2 Math, Science and SAT . /BaseFont/BPHBTR+CMMI12 /FontDescriptor 8 0 R (answer). Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Level up on all the skills in this unit and collect up to 2000 Mastery points! 24 0 obj Integral Test In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges. Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. Estimating the Value of a Series In this section we will discuss how the Integral Test, Comparison Test, Alternating Series Test and the Ratio Test can, on occasion, be used to estimating the value of an infinite series. >> 531.3 531.3 531.3] The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. stream /Length 465 Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses. We use the geometric, p-series, telescoping series, nth term test, integral test, direct comparison, limit comparison, ratio test, root test, alternating series test, and the test. Series Infinite geometric series: Series nth-term test: Series Integral test: Series Harmonic series and p-series: Series Comparison tests: . Chapters include Linear The steps are terms in the sequence. Remark. 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 n = 1 n 2 + 2 n n 3 + 3 n . Calculus 2. It turns out the answer is no. }\right\}_{n=0}^{\infty}\) converges or diverges. Maclaurin series of e, sin(x), and cos(x). )Ltgx?^eaT'&+n+hN4*D^UR!8UY@>LqS%@Cp/-12##DR}miBw6"ja+WjU${IH$5j!j-I1 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 If you'd like a pdf document containing the solutions the download tab above contains links to pdf's containing the solutions for the full book, chapter and section. (answer), Ex 11.2.7 Compute \(\sum_{n=0}^\infty {3^{n+1}\over 7^{n+1}}\). Free Practice Test Instructions: Choose your answer to the question and click 'Continue' to see how you did. (1 point) Is the integral Z 1 1 1 x2 dx an improper integral? /Widths[663.6 885.4 826.4 736.8 708.3 795.8 767.4 826.4 767.4 826.4 767.4 619.8 590.3 12 0 obj 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 Convergence/Divergence of Series In this section we will discuss in greater detail the convergence and divergence of infinite series. Parametric Equations and Polar Coordinates, 9.5 Surface Area with Parametric Equations, 9.11 Arc Length and Surface Area Revisited, 10.7 Comparison Test/Limit Comparison Test, 12.8 Tangent, Normal and Binormal Vectors, 13.3 Interpretations of Partial Derivatives, 14.1 Tangent Planes and Linear Approximations, 14.2 Gradient Vector, Tangent Planes and Normal Lines, 15.3 Double Integrals over General Regions, 15.4 Double Integrals in Polar Coordinates, 15.6 Triple Integrals in Cylindrical Coordinates, 15.7 Triple Integrals in Spherical Coordinates, 16.5 Fundamental Theorem for Line Integrals, 3.8 Nonhomogeneous Differential Equations, 4.5 Solving IVP's with Laplace Transforms, 7.2 Linear Homogeneous Differential Equations, 8. 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 Consider the series n a n. Divergence Test: If lim n a n 0, then n a n diverges. L7s[AQmT*Z;HK%H0yqt1r8 Choose your answer to the question and click 'Continue' to see how you did. (answer), Ex 11.9.4 Find a power series representation for \( 1/(1-x)^3\). Calculus II - Sequences and Series Flashcards | Quizlet %PDF-1.5 % Math C185: Calculus II (Tran) 6: Sequences and Series 6.5: Comparison Tests 6.5E: Exercises for Comparison Test Expand/collapse global location 6.5E: Exercises for Comparison Test . Most sections should have a range of difficulty levels in the problems although this will vary from section to section. For each function, find the Maclaurin series or Taylor series centered at $a$, and the radius of convergence. 590.3 767.4 795.8 795.8 1091 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 441.3 461.2 353.6 557.3 473.4 699.9 556.4 477.4 454.9 312.5 377.9 623.4 489.6 272] Strategies for Testing Series - University of Texas at Austin (answer), Ex 11.2.4 Compute \(\sum_{n=0}^\infty {4\over (-3)^n}- {3\over 3^n}\). Defining convergent and divergent infinite series, Determining absolute or conditional convergence, Finding Taylor polynomial approximations of functions, Radius and interval of convergence of power series, Finding Taylor or Maclaurin series for a function. endobj In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. endobj Then click 'Next Question' to answer the next question. 9 0 obj 1 2, 1 4, 1 8, Sequences of values of this type is the topic of this rst section. Comparison Test/Limit Comparison Test In this section we will discuss using the Comparison Test and Limit Comparison Tests to determine if an infinite series converges or diverges. /BaseFont/UNJAYZ+CMR12 We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Final: all from 02/05 and 03/11 exams (except work, separation of variables, and probability) plus sequences, series, convergence tests, power series, Taylor series. Solution. (answer), Ex 11.2.9 Compute \(\sum_{n=1}^\infty {3^n\over 5^{n+1}}\). Sequences & Series in Calculus Chapter Exam. 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 If you're seeing this message, it means we're having trouble loading external resources on our website. To use the Geometric Series formula, the function must be able to be put into a specific form, which is often impossible. /Widths[611.8 816 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 707.2 571.2 544 544 70 terms. 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 (answer), Ex 11.10.10 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( xe^{-x}\). stream /LastChar 127 /Name/F3 /FirstChar 0 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 Ex 11.11.5 Show that \(e^x\) is equal to its Taylor series for all \(x\) by showing that the limit of the error term is zero as \(N\) approaches infinity. Parametric Equations and Polar Coordinates, 9.5 Surface Area with Parametric Equations, 9.11 Arc Length and Surface Area Revisited, 10.7 Comparison Test/Limit Comparison Test, 12.8 Tangent, Normal and Binormal Vectors, 13.3 Interpretations of Partial Derivatives, 14.1 Tangent Planes and Linear Approximations, 14.2 Gradient Vector, Tangent Planes and Normal Lines, 15.3 Double Integrals over General Regions, 15.4 Double Integrals in Polar Coordinates, 15.6 Triple Integrals in Cylindrical Coordinates, 15.7 Triple Integrals in Spherical Coordinates, 16.5 Fundamental Theorem for Line Integrals, 3.8 Nonhomogeneous Differential Equations, 4.5 Solving IVP's with Laplace Transforms, 7.2 Linear Homogeneous Differential Equations, 8. /BaseFont/SFGTRF+CMSL12 PDF Read Free Answers To Algebra 2 Practice B Ellipses Differentiate u to find du, and integrate dv to find v. Use the formula: Evaluate the right side of this equation to solve the integral. UcTIjeB#vog-TM'FaTzG(:k-BNQmbj}'?^h<=XgS/]o4Ilv%Jm Integral Test: If a n = f ( n), where f ( x) is a non-negative non-increasing function, then. in calculus coursesincluding Calculus, Calculus II, Calculus III, AP Calculus and Precalculus. 826.4 531.3 958.7 1076.8 826.4 295.1 295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 /Name/F2 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 Remark. In exercises 3 and 4, do not attempt to determine whether the endpoints are in the interval of convergence. Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. 21 terms. n = 1 n2 + 2n n3 + 3n2 + 1. Given item A, which of the following would be the value of item B? 556.5 425.2 527.8 579.5 613.4 636.6 609.7 458.2 577.1 808.9 505 354.2 641.4 979.2 /Filter /FlateDecode Power Series In this section we will give the definition of the power series as well as the definition of the radius of convergence and interval of convergence for a power series. 590.3 885.4 885.4 295.1 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 hbbd```b``~"A$" "Y`L6`RL,-`sA$w64= f[" RLMu;@jAl[`3H^Ne`?$4 /Widths[777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 Then click 'Next Question' to answer the . (answer), Ex 11.3.12 Find an \(N\) so that \(\sum_{n=2}^\infty {1\over n(\ln n)^2}\) is between \(\sum_{n=2}^N {1\over n(\ln n)^2}\) and \(\sum_{n=2}^N {1\over n(\ln n)^2} + 0.005\). Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. If L = 1, then the test is inconclusive. 883.8 992.6 761.6 272 272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 Infinite series are sums of an infinite number of terms. Absolute and conditional convergence. Other sets by this creator. More on Sequences In this section we will continue examining sequences. 11.E: Sequences and Series (Exercises) These are homework exercises to accompany David Guichard's "General Calculus" Textmap. Calculus II - Series - The Basics (Practice Problems) - Lamar University The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Then click 'Next Question' to answer the next question. (answer), Ex 11.2.8 Compute \(\sum_{n=1}^\infty \left({3\over 5}\right)^n\). 1. /FontDescriptor 17 0 R << << 816 816 272 299.2 489.6 489.6 489.6 489.6 489.6 792.7 435.2 489.6 707.2 761.6 489.6 The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion.The test is only sufficient, not necessary, so some convergent . Ex 11.1.3 Determine whether {n + 47 n} . 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 Chapter 10 : Series and Sequences. nth-term test. Worksheets. << Calculus II - Series & Sequences (Practice Problems) - Lamar University PDF Schaums Outline Of Differential Equations 4th Edition Schaums Outline 833.3 833.3 833.3 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 << My calculus 2 exam on sequence, infinite series & power seriesThe exam: https://bit.ly/36OHYcsAll the convergence tests: https://bit.ly/2IzqokhBest friend an. 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 252 0 obj <>stream copyright 2003-2023 Study.com. PDF FINAL EXAM CALCULUS 2 - Department of Mathematics Which of the following is the 14th term of the sequence below? Part II. Comparison tests. 555.6 577.8 577.8 597.2 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 << Strip out the first 3 terms from the series \( \displaystyle \sum\limits_{n = 1}^\infty {\frac{{{2^{ - n}}}}{{{n^2} + 1}}} \). Comparison Test: This applies . What is the sum of all the even integers from 2 to 250? We will examine Geometric Series, Telescoping Series, and Harmonic Series. endstream endobj startxref Determine whether the series converge or diverge. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. stream Ex 11.10.8 Find the first four terms of the Maclaurin series for \(\tan x\) (up to and including the \( x^3\) term). Ex 11.5.1 \(\sum_{n=1}^\infty {1\over 2n^2+3n+5} \) (answer), Ex 11.5.2 \(\sum_{n=2}^\infty {1\over 2n^2+3n-5} \) (answer), Ex 11.5.3 \(\sum_{n=1}^\infty {1\over 2n^2-3n-5} \) (answer), Ex 11.5.4 \(\sum_{n=1}^\infty {3n+4\over 2n^2+3n+5} \) (answer), Ex 11.5.5 \(\sum_{n=1}^\infty {3n^2+4\over 2n^2+3n+5} \) (answer), Ex 11.5.6 \(\sum_{n=1}^\infty {\ln n\over n}\) (answer), Ex 11.5.7 \(\sum_{n=1}^\infty {\ln n\over n^3}\) (answer), Ex 11.5.8 \(\sum_{n=2}^\infty {1\over \ln n}\) (answer), Ex 11.5.9 \(\sum_{n=1}^\infty {3^n\over 2^n+5^n}\) (answer), Ex 11.5.10 \(\sum_{n=1}^\infty {3^n\over 2^n+3^n}\) (answer). A summary of all the various tests, as well as conditions that must be met to use them, we discussed in this chapter are also given in this section. << 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 /Widths[611.8 816 761.6 679.6 652.8 734 707.2 761.6 707.2 761.6 707.2 571.2 544 544 Sequences review (practice) | Series | Khan Academy You may also use any of these materials for practice. Indiana Core Assessments Mathematics: Test Prep & Study Guide. /Widths[606.7 816 748.3 679.6 728.7 811.3 765.8 571.2 652.8 598 757.6 622.8 552.8 Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. We will also briefly discuss how to determine if an infinite series will converge or diverge (a more in depth discussion of this topic will occur in the next section). >> /Length 569 sCA%HGEH[ Ah)lzv<7'9&9X}xbgY[ xI9i,c_%tz5RUam\\6(ke9}Yv`B7yYdWrJ{KZVUYMwlbN_>[wle\seUy24P,PyX[+l\c $w^rvo]cYc@bAlfi6);;wOF&G_. /Name/F6 We will also illustrate how the Ratio Test and Root Test can be used to determine the radius and interval of convergence for a power series. >> /Type/Font !A1axw)}p]WgxmkFftu Which of the following represents the distance the ball bounces from the first to the seventh bounce with sigma notation? Math 1242: Calculus II - University of North Carolina at Charlotte /LastChar 127 We will also give the Divergence Test for series in this section. 18 0 obj After each bounce, the ball reaches a height that is 2/3 of the height from which it previously fell. /FontDescriptor 14 0 R Khan Academy is a 501(c)(3) nonprofit organization. We will also give many of the basic facts and properties well need as we work with sequences. Ex 11.1.1 Compute \(\lim_{x\to\infty} x^{1/x}\). With an outline format that facilitates quick and easy review, Schaum's Outline of Calculus, Seventh Edition helps you understand basic concepts and get the extra practice you need to excel in these courses. )^2\over n^n}(x-2)^n\) (answer), Ex 11.8.6 \(\sum_{n=1}^\infty {(x+5)^n\over n(n+1)}\) (answer), Ex 11.9.1 Find a series representation for \(\ln 2\). /LastChar 127 The Integral Test can be used on a infinite series provided the terms of the series are positive and decreasing. stream /BaseFont/CQGOFL+CMSY10 What is the radius of convergence? Power Series and Functions In this section we discuss how the formula for a convergent Geometric Series can be used to represent some functions as power series. Accessibility StatementFor more information contact us atinfo@libretexts.org. Which one of these sequences is a finite sequence? 665 570.8 924.4 812.6 568.1 670.2 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 Math 129 - Calculus II Worksheets - University of Arizona For problems 1 3 perform an index shift so that the series starts at \(n = 3\). (answer), Ex 11.2.2 Explain why \(\sum_{n=1}^\infty {5\over 2^{1/n}+14}\) diverges. << The Alternating Series Test can be used only if the terms of the 5.3.3 Estimate the value of a series by finding bounds on its remainder term. Some infinite series converge to a finite value. Series are sums of multiple terms. Ex 11.1.2 Use the squeeze theorem to show that limn n! >> PDF M 172 - Calculus II - Chapter 10 Sequences and Series A brick wall has 60 bricks in the first row, but each row has 3 fewer bricks than the previous one. Which equation below represents a geometric sequence? Taylor Series In this section we will discuss how to find the Taylor/Maclaurin Series for a function. Level up on all the skills in this unit and collect up to 2000 Mastery points! Divergence Test. Example 1. Series are sums of multiple terms. Which of the following is the 14th term of the sequence below? PDF Calculus II Series - Things to Consider - California State University AP Calculus AB and BC: Chapter 9 -Infinite Sequences and Series : 9.2 Calculus 2 | Math | Khan Academy For each of the following series, determine which convergence test is the best to use and explain why. All rights reserved. endobj About this unit. /LastChar 127 I have not learned series solutions nor special functions which I see is the next step in this chapter) Linear Algebra (self-taught from Hoffman and Kunze. (answer). 777.8 444.4 444.4 444.4 611.1 777.8 777.8 777.8 777.8] . (answer), Ex 11.3.11 Find an \(N\) so that \(\sum_{n=1}^\infty {\ln n\over n^2}\) is between \(\sum_{n=1}^N {\ln n\over n^2}\) and \(\sum_{n=1}^N {\ln n\over n^2} + 0.005\). Quiz 2: 8 questions Practice what you've learned, and level up on the above skills. nn = 0. Learning Objectives. Sequences and Numerical series. 26 0 obj 31 terms. Course summary; . We will focus on the basic terminology, limits of sequences and convergence of sequences in this section.

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