Convergence of a series - Printable Version +- OMath! (http://math.elinkage.net) +-- Forum: Math Forums (/forumdisplay.php?fid=4) +--- Forum: Analysis (/forumdisplay.php?fid=10) +--- Thread: Convergence of a series (/showthread.php?tid=73) 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