Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. Given that \( \displaystyle \sum\limits_{n = 0}^\infty {\frac{1}{{{n^3} + 1}}} = 1.6865\) determine the value of \( \displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{{n^3} + 1}}} \). S.QBt'(d|/"XH4!qbnEriHX)Gs2qN/G jq8$$< When given a sum a[n], if the limit as n-->infinity does not exist or does not equal 0, the sum diverges. /FirstChar 0 >> >> 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 /FirstChar 0 Given item A, which of the following would be the value of item B? A review of all series tests. (answer), Ex 11.9.3 Find a power series representation for \( 2/(1-x)^3\). Use the Comparison Test to determine whether each series in exercises 1 - 13 converges or diverges. At this time, I do not offer pdf's for solutions to individual problems. Each term is the product of the two previous terms. Good luck! 1. /BaseFont/VMQJJE+CMR8 Ex 11.6.1 \(\sum_{n=1}^\infty (-1)^{n-1}{1\over 2n^2+3n+5}\) (answer), Ex 11.6.2 \(\sum_{n=1}^\infty (-1)^{n-1}{3n^2+4\over 2n^2+3n+5}\) (answer), Ex 11.6.3 \(\sum_{n=1}^\infty (-1)^{n-1}{\ln n\over n}\) (answer), Ex 11.6.4 \(\sum_{n=1}^\infty (-1)^{n-1} {\ln n\over n^3}\) (answer), Ex 11.6.5 \(\sum_{n=2}^\infty (-1)^n{1\over \ln n}\) (answer), Ex 11.6.6 \(\sum_{n=0}^\infty (-1)^{n} {3^n\over 2^n+5^n}\) (answer), Ex 11.6.7 \(\sum_{n=0}^\infty (-1)^{n} {3^n\over 2^n+3^n}\) (answer), Ex 11.6.8 \(\sum_{n=1}^\infty (-1)^{n-1} {\arctan n\over n}\) (answer). Calculus II - Sequences and Series Flashcards | Quizlet (answer), Ex 11.10.9 Use a combination of Maclaurin series and algebraic manipulation to find a series centered at zero for \( x\cos (x^2)\). Integral Test In this section we will discuss using the Integral Test to determine if an infinite series converges or diverges. All other trademarks and copyrights are the property of their respective owners. 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al. 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 MATH 126 Medians and Such. The practice tests are composed >> Each term is the sum of the previous two terms. Calculus (single and multi-variable) Ordinary Differential equations (upto 2nd order linear with Laplace transforms, including Dirac Delta functions and Fourier Series. 1277.8 555.6 1000 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 238 0 obj <>/Filter/FlateDecode/ID[<09CA7BCBAA751546BDEE3FEF56AF7BFA>]/Index[207 46]/Info 206 0 R/Length 137/Prev 582846/Root 208 0 R/Size 253/Type/XRef/W[1 3 1]>>stream PDF Calculus II Series - Things to Consider - California State University Sequences review (practice) | Series | Khan Academy (answer), Ex 11.1.5 Determine whether \(\left\{{n+47\over\sqrt{n^2+3n}}\right\}_{n=1}^{\infty}\) converges or diverges. We will illustrate how we can find a series representation for indefinite integrals that cannot be evaluated by any other method. /Length 200 Then click 'Next Question' to answer the next question. When you have completed the free practice test, click 'View Results' to see your results. Then click 'Next Question' to answer the next question. /Filter /FlateDecode Each review chapter is packed with equations, formulas, and examples with solutions, so you can study smarter and score a 5! Quiz 1: 5 questions Practice what you've learned, and level up on the above skills. (a) $\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}$ (b) $\sum_{n=1}^{\infty}(-1)^n \frac{n}{2 n-1}$ 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. /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 %PDF-1.2 For problems 1 3 perform an index shift so that the series starts at \(n = 3\). /LastChar 127 /FontDescriptor 17 0 R Don't all infinite series grow to infinity? In other words, a series is the sum of a sequence. Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses. 5.3.1 Use the divergence test to determine whether a series converges or diverges. (answer), Ex 11.2.6 Compute \(\sum_{n=0}^\infty {4^{n+1}\over 5^n}\). PDF Ap Calculus Ab Bc Kelley Copy - gny.salvationarmy.org Sequences can be thought of as functions whose domain is the set of integers. (answer). (answer), Ex 11.2.2 Explain why \(\sum_{n=1}^\infty {5\over 2^{1/n}+14}\) diverges. For each function, find the Maclaurin series or Taylor series centered at $a$, and the radius of convergence. 17 0 obj %PDF-1.5 If you're seeing this message, it means we're having trouble loading external resources on our website. 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 Integral test. 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 copyright 2003-2023 Study.com. /FirstChar 0 Calculus II-Sequences and Series. How many bricks are in the 12th row? << Chapters include Linear Ex 11.8.1 \(\sum_{n=0}^\infty n x^n\) (answer), Ex 11.8.2 \(\sum_{n=0}^\infty {x^n\over n! 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 Special Series In this section we will look at three series that either show up regularly or have some nice properties that we wish to discuss. 777.8 444.4 444.4 444.4 611.1 777.8 777.8 777.8 777.8] >> /FirstChar 0 Then click 'Next Question' to answer the next question. PDF Read Free Answers To Algebra 2 Practice B Ellipses 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. Find the radius and interval of convergence for each of the following series: Solution (a) We apply the Ratio Test to the series n = 0 | x n n! 666.7 1000 1000 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 Find the sum of the following geometric series: The formula for a finite geometric series is: Which of these is an infinite sequence of all the non-zero even numbers beginning at number 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. Our mission is to provide a free, world-class education to anyone, anywhere. Note that some sections will have more problems than others and some will have more or less of a variety of problems. /Type/Font >> /Subtype/Type1 11.E: Sequences and Series (Exercises) - Mathematics LibreTexts 68 0 obj % stream Ex 11.1.3 Determine whether \(\{\sqrt{n+47}-\sqrt{n}\}_{n=0}^{\infty}\) converges or diverges. Calculus II - Series & Sequences (Practice Problems) - Lamar University Sequences & Series in Calculus Chapter Exam - Study.com Example 1. Worksheets. If it converges, compute the limit. Proofs for both tests are also given. Learning Objectives. (answer). The numbers used come from a sequence. /Name/F4 A proof of the Alternating Series Test is also given. (answer). Sequences and Series for Calculus Chapter Exam - Study.com (1 point) Is the integral Z 1 1 1 x2 dx an improper integral? 207 0 obj <> endobj Math 129 - Calculus II Worksheets - University of Arizona 5.3.3 Estimate the value of a series by finding bounds on its remainder term. Published by Wiley. 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 . PDF Schaums Outline Of Differential Equations 4th Edition Schaums Outline If it converges, compute the limit. /LastChar 127 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2 489.6 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. >> 777.8 777.8] The following is a list of worksheets and other materials related to Math 129 at the UA. Ex 11.7.3 Compute \(\lim_{n\to\infty} |a_n|^{1/n}\) for the series \(\sum 1/n^2\). Then click 'Next Question' to answer the next question. Which rule represents the nth term in the sequence 9, 16, 23, 30? If it converges, compute the limit. Series The Basics In this section we will formally define an infinite series. 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/F3 Calc II: Practice Final Exam 5 and our series converges because P nbn is a p-series with p= 4=3 >1: (b) X1 n=1 lnn n3 Set f(x) = lnx x3 and check that f0= 43x lnx+ x 4 <0 stream (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 \(\sum_{n=2}^N {1\over n(\ln n)^2} + 0.005\). endobj (answer), Ex 11.2.4 Compute \(\sum_{n=0}^\infty {4\over (-3)^n}- {3\over 3^n}\). (answer), Ex 11.2.1 Explain why \(\sum_{n=1}^\infty {n^2\over 2n^2+1}\) diverges. For problems 1 - 3 perform an index shift so that the series starts at n = 3 n = 3. endstream endobj 208 0 obj <. Other sets by this creator. It turns out the answer is no. /Type/Font Strategies for Testing Series - University of Texas at Austin What is the radius of convergence? 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.
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