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cnn! nn 59. Let S = Σ where c is a constant. n=1 (a) Prove that S converges absolutely if |c| e. en n! (b) It is known that lim √27. Verify this numerically. n→∞nn+1/2 (c) Use the Limit Comparison Test to prove that S diverges for c = e.

cnn! nn 59. Let S = Σ where c is a constant. n=1 (a) Prove that S converges absolutely if |c| e. en n! (b) It is known that lim √27. Verify this numerically. n→∞nn+1/2 (c) Use the Limit Comparison Test to prove that S diverges for c = e.

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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59. Let S = cnn! nn 9 where c is a constant. n=1 (a) Prove that S converges absolutely if |c| < e and diverges if |c| > e. en n! (b) It is known that lim √27. Verify this numerically. n→∞nn+1/2 (c) Use the Limit Comparison Test to prove that S diverges for c = e. =
Transcribed Image Text:59. Let S = cnn! nn 9 where c is a constant. n=1 (a) Prove that S converges absolutely if |c| < e and diverges if |c| > e. en n! (b) It is known that lim √27. Verify this numerically. n→∞nn+1/2 (c) Use the Limit Comparison Test to prove that S diverges for c = e. =
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