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Convergence of a series - Printable Version

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Convergence of a series - elim - 05-12-2010 11:25 AM

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 \(\sum\limits_{k=1}^\infty |b_{k}| < \infty\)


RE: Convergence of a series - elim - 05-26-2010 07:25 AM

\(\sum_{k=1}^n |b_k| \le 2\sum_{k=1}^n \frac{2n-k}{2n}|b_k| \le 2\sum_{k=1}^{2n} \frac{2n-k}{2n} |b_k| \le 2M\)


Other Solutions? - elim - 09-04-2012 07:51 PM

Welcome to other solutions