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A. Divergence Test B. Geometric Series C. p-Series D. Comparison Test E. Alternating Series Test F. Ratio Test • Σ(√A)* a. n=1 b. Σ2-sin(1/n) C. n=1 ∞ n=1 α. Σ(-1) n=0 (−1)n+1 +3 e. an = ∞ f. Σ n=1 3 10n n! n 1 2n - 1

A. Divergence Test B. Geometric Series C. p-Series D. Comparison Test E. Alternating Series Test F. Ratio Test • Σ(√A)* a. n=1 b. Σ2-sin(1/n) C. n=1 ∞ n=1 α. Σ(-1) n=0 (−1)n+1 +3 e. an = ∞ f. Σ n=1 3 10n n! n 1 2n - 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Match the series or sequence with the appropriate test or series to determine whether the series converges, i.e which test or series would you use to determine convergence?
**Series and Tests** For each type of series test listed below, match it to the corresponding series expression: **A. Divergence Test** ______ **B. Geometric Series** ______ **C. p-Series** ______ **D. Comparison Test** ______ **E. Alternating Series Test** ______ **F. Ratio Test** ______ **Series Expressions:** - **a.** \(\sum_{n=1}^{\infty} \left(\sqrt{\frac{1}{n}}\right)^3\) - **b.** \(\sum_{n=1}^{\infty} 2^{-\sin(1/n)}\) - **c.** \(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{\sqrt{n + 3}}\) - **d.** \(\sum_{n=0}^{\infty} \left(-\frac{1}{2}\right)^n\) - **e.** \(a_n = \frac{10^n}{n!}\) - **f.** \(\sum_{n=1}^{\infty} \frac{1}{2n - 1}\) Understand each test and match it to the series that it can evaluate.
Transcribed Image Text:**Series and Tests** For each type of series test listed below, match it to the corresponding series expression: **A. Divergence Test** ______ **B. Geometric Series** ______ **C. p-Series** ______ **D. Comparison Test** ______ **E. Alternating Series Test** ______ **F. Ratio Test** ______ **Series Expressions:** - **a.** \(\sum_{n=1}^{\infty} \left(\sqrt{\frac{1}{n}}\right)^3\) - **b.** \(\sum_{n=1}^{\infty} 2^{-\sin(1/n)}\) - **c.** \(\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{\sqrt{n + 3}}\) - **d.** \(\sum_{n=0}^{\infty} \left(-\frac{1}{2}\right)^n\) - **e.** \(a_n = \frac{10^n}{n!}\) - **f.** \(\sum_{n=1}^{\infty} \frac{1}{2n - 1}\) Understand each test and match it to the series that it can evaluate.
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