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For which of the following series does the alternating test ensure convergence? D[(-1)" In ² (cos - -) n=1 Pi n=1 )(−1)” arctan(7n) Σ(-1)" I "+1 n n=1 Σ(-1)" n=1 Σ(-1)" n=0 1 )(−1)" arctan = n n=1 2n - 1 2n + 1 n=1 3n 1 (-1) (3-¹)" Σ(-1)", (−1)n (n!) ² (2n)! n=0 [(-1)" (¹²) " 5 n=0 n Σ(−1)n (n²)! n=0 (2n)!

For which of the following series does the alternating test ensure convergence? D[(-1)" In ² (cos - -) n=1 Pi n=1 )(−1)” arctan(7n) Σ(-1)" I "+1 n n=1 Σ(-1)" n=1 Σ(-1)" n=0 1 )(−1)" arctan = n n=1 2n - 1 2n + 1 n=1 3n 1 (-1) (3-¹)" Σ(-1)", (−1)n (n!) ² (2n)! n=0 [(-1)" (¹²) " 5 n=0 n Σ(−1)n (n²)! n=0 (2n)!

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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For which of the following series does the alternating test ensure convergence? (-1)" In? (cos 7) ΣΕ n=1 Σ(-1)" arctan(πη) n=1 Σ(-1)" In n=1 Σ(-1)" n=1 ΟΣ Σ(1)" n=0 n+1 η 2η – 1 2n + 1 1 Σ(-1)" arctan = η n=1 ΟΣ 1) (31) n=1 (n!)² (2η)! Σ (-1)". n=0 [(-1)^(-—-—- )" (7)" 5 n=0 Σ(−1)n (n²)! n=0 (2n)! n
Transcribed Image Text:For which of the following series does the alternating test ensure convergence? (-1)" In? (cos 7) ΣΕ n=1 Σ(-1)" arctan(πη) n=1 Σ(-1)" In n=1 Σ(-1)" n=1 ΟΣ Σ(1)" n=0 n+1 η 2η – 1 2n + 1 1 Σ(-1)" arctan = η n=1 ΟΣ 1) (31) n=1 (n!)² (2η)! Σ (-1)". n=0 [(-1)^(-—-—- )" (7)" 5 n=0 Σ(−1)n (n²)! n=0 (2n)! n
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