n = 1 n 2 + 2 n n 3 + 3 n . /FirstChar 0 (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 \(\sum_{n=1}^N {\ln n\over n^2} + 0.005\). n a n converges if and only if the integral 1 f ( x) d x converges. S.QBt'(d|/"XH4!qbnEriHX)Gs2qN/G jq8$$< 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 Calculus II - Series - The Basics (Practice Problems) - Lamar University endobj !A1axw)}p]WgxmkFftu Ex 11.1.1 Compute \(\lim_{x\to\infty} x^{1/x}\). (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 \(\sum_{n=2}^N {1\over n(\ln n)^2} + 0.005\). Indiana Core Assessments Mathematics: Test Prep & Study Guide. >> The Alternating Series Test can be used only if the terms of the series alternate in sign. OR sequences are lists of numbers, where the numbers may or may not be determined by a pattern. All rights reserved. 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. endobj 207 0 obj
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<< Worksheets. (answer). If a geometric series begins with the following term, what would the next term be? 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 The steps are terms in the sequence. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If it con-verges, nd the limit. We will also give many of the basic facts, properties and ways we can use to manipulate a series. 21 terms. To use integration by parts in Calculus, follow these steps: Decompose the entire integral (including dx) into two factors. Published by Wiley. 777.8 444.4 444.4 444.4 611.1 777.8 777.8 777.8 777.8] (You may want to use Sage or a similar aid.) Given item A, which of the following would be the value of item B? 238 0 obj
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Chapters include Linear Chapter 10 : Series and Sequences. /Length 200 Part II. 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. Question 5 5. % 1. 5.3.1 Use the divergence test to determine whether a series converges or diverges. endstream Bottom line -- series are just a lot of numbers added together. endobj Integral Test: If a n = f ( n), where f ( x) is a non-negative non-increasing function, then. It turns out the answer is no. )Ltgx?^eaT'&+n+hN4*D^UR!8UY@>LqS%@Cp/-12##DR}miBw6"ja+WjU${IH$5j!j-I1 Sequences and Series: Comparison Test; Taylor Polynomials Practice; Power Series Practice; Calculus II Arc Length of Parametric Equations; 3 Dimensional Lines; Vectors Practice; Meanvariance SD - Mean Variance; Preview text. Sequences can be thought of as functions whose domain is the set of integers. 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). Math Journey: Calculus, ODEs, Linear Algebra and Beyond stream 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 MULTIPLE CHOICE: Circle the best answer. Good luck! You may also use any of these materials for practice. Some infinite series converge to a finite value. A proof of the Alternating Series Test is also given. nth-term test. 9 0 obj Convergence/Divergence of Series In this section we will discuss in greater detail the convergence and divergence of infinite series. %PDF-1.5 Then click 'Next Question' to answer the next question. 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\newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\). /FirstChar 0 Which of the following is the 14th term of the sequence below? Ex 11.1.3 Determine whether \(\{\sqrt{n+47}-\sqrt{n}\}_{n=0}^{\infty}\) converges or diverges. 507.9 433.7 395.4 427.7 483.1 456.3 346.1 563.7 571.2 589.1 483.8 427.7 555.4 505 Absolute and conditional convergence. /Filter /FlateDecode Then determine if the series converges or diverges. 5.3.2 Use the integral test to determine the convergence of a series. Remark. Khan Academy is a 501(c)(3) nonprofit organization. AP Calculus AB and BC: Chapter 9 -Infinite Sequences and Series : 9.2 Harmonic series and p-series. 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 PDF Arithmetic Sequences And Series Practice Problems /Type/Font 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 Calculus II - Series & Sequences (Practice Problems) - Lamar University Which is the infinite sequence starting with 1 where each number is the previous number times 3? (a) $\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}$ (b) $\sum_{n=1}^{\infty}(-1)^n \frac{n}{2 n-1}$ /Type/Font A brick wall has 60 bricks in the first row, but each row has 3 fewer bricks than the previous one. 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. Which of the sequences below has the recursive rule where each number is the previous number times 2? For each function, find the Maclaurin series or Taylor series centered at $a$, and the radius of convergence. A ball is dropped from an unknown height (h) and it repeatedly bounces on the floor. 17 0 obj Quiz 1: 5 questions Practice what you've learned, and level up on the above skills. 531.3 531.3 531.3]
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