I did them in excel, found the following values.
\sum_{n=0}^{+\infty}{\frac{n}{2^n}} = 2/1
\sum_{n=0}^{+\infty}{\frac{n}{3^n}} = 3/4
\sum_{n=0}^{+\infty}{\frac{n}{4^n}} = 4/9
\sum_{n=0}^{+\infty}{\frac{n}{5^n}} = 5/16
and on...
So i figured out that i can find where any of...
I know that the following serie converges to 2 (did in excel), still I would like to know how i can prove it step by step it.
∞
∑ n/2^n
n=1
I tried (n+1)/(2^(n+1))/(n/2^n) still I'm finding 1/2, not the 2.
Any thoughts?