Convergence of a series

05122010, 11:25 AM
(This post was last modified: 05122010 11:27 AM by elim.)
Post: #1




Convergence of a series
Suppose \(\left\{b_{k}\right\}\) has the property that:
\(\sum\limits_{k=1}^n \frac{nk}{n} b_{k} \leq M \quad (\forall n)\quad\) Show that \(\sum\limits_{k=1}^\infty b_{k} < \infty\) 

05262010, 07:25 AM
Post: #2




RE: Convergence of a series
\(\sum_{k=1}^n b_k \le 2\sum_{k=1}^n \frac{2nk}{2n}b_k \le 2\sum_{k=1}^{2n} \frac{2nk}{2n} b_k \le 2M\)


09042012, 07:51 PM
(This post was last modified: 09042012 09:47 PM by admin.)
Post: #3




Other Solutions?
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