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2. Assume that ak converges and (bn) is bounded. Prove that Σakbk converges. (hint: use Cauchy criterion) = 0, then there is a subsequence (ank) of (an) so 3. Assume lim inf|an| that any converges absolutely.

2. Assume that ak converges and (bn) is bounded. Prove that Σakbk converges. (hint: use Cauchy criterion) = 0, then there is a subsequence (ank) of (an) so 3. Assume lim inf|an| that any converges absolutely.

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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Correction: Q2 sum a_k is absolutely convergent.

2. Assume that \(\sum a_k\) converges and \((b_n)\) is bounded. Prove that \(\sum a_k b_k\) converges. (hint: use Cauchy criterion) 3. Assume \(\lim \inf |a_n| = 0\), then there is a subsequence \((a_{n_k})\) of \((a_n)\) so that \(\sum a_{n_k}\) converges absolutely.
Transcribed Image Text:2. Assume that \(\sum a_k\) converges and \((b_n)\) is bounded. Prove that \(\sum a_k b_k\) converges. (hint: use Cauchy criterion) 3. Assume \(\lim \inf |a_n| = 0\), then there is a subsequence \((a_{n_k})\) of \((a_n)\) so that \(\sum a_{n_k}\) converges absolutely.
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