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Convergence of a series
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05-12-2010, 11:25 AM
(This post was last modified: 05-12-2010 11:27 AM by elim.)
Post: #1
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Convergence of a series
Suppose \(\left\{b_{k}\right\}\) has the property that:
\(\sum\limits_{k=1}^n \frac{n-k}{n} |b_{k}| \leq M \quad (\forall n)\quad\) Show that \(\sum\limits_{k=1}^\infty |b_{k}| < \infty\) |
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05-26-2010, 07:25 AM
Post: #2
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RE: Convergence of a series
\(\sum_{k=1}^n |b_k| \le 2\sum_{k=1}^n \frac{2n-k}{2n}|b_k| \le 2\sum_{k=1}^{2n} \frac{2n-k}{2n} |b_k| \le 2M\)
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09-04-2012, 07:51 PM
(This post was last modified: 09-04-2012 09:47 PM by admin.)
Post: #3
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Other Solutions?
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