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Find a series ak that satisfies each of the following conditions or explain why it is not possible. k=1 (a) lim ak = 0 and Σak diverges. k→∞ k=1 (b) lim ak = 0 and a converges. k→∞ k=1 (c) lim ak = 0 and ak = 3 k→∞ k=1

Find a series ak that satisfies each of the following conditions or explain why it is not possible. k=1 (a) lim ak = 0 and Σak diverges. k→∞ k=1 (b) lim ak = 0 and a converges. k→∞ k=1 (c) lim ak = 0 and ak = 3 k→∞ k=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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Find a series \(\sum_{k=1}^{\infty} a_k\) that satisfies each of the following conditions or explain why it is not possible. (a) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k\) diverges. (b) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k\) converges. (c) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k = 3\).
Transcribed Image Text:Find a series \(\sum_{k=1}^{\infty} a_k\) that satisfies each of the following conditions or explain why it is not possible. (a) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k\) diverges. (b) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k\) converges. (c) \(\lim_{k \to \infty} a_k = 0\) and \(\sum_{k=1}^{\infty} a_k = 3\).
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