Thursday, 9 July 2015

real analysis - the sum of the series $sum frac{n}{2^{n}}$

the sum of the series $\sum_{n=1}^\infty \frac{1}{2^{n}}$ is 1. It is easy to find since it is a g.p. the series $\sum_{n=1}^\infty \frac{n}{2^{n}}$ is convergent by ratio test. How will find the infinite sum? I am trying to rearrange the terms and to use the rearrangement theorem, but I can't complete

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...