# Math Help - find the sum of series

1. ## find the sum of series

starting with geometric series sigma from n=0 to infinity of x^n find the sum of the series of sigma from n= 1 to infinity of n(x)^(n-1) lxl<1

b) find the sum of each of the following series,
1) sigma from n = 1 to infinity nX^n, lxl<1
2) sigma from n=1 to infity of n/2^n

2. Originally Posted by twilightstr
starting with geometric series sigma from n=0 to infinity of x^n find the sum of the series of sigma from n= 1 to infinity of n(x)^(n-1) lxl<1

b) find the sum of each of the following series,
1) sigma from n=1 to infinity nX^n, lxl<1
2) sigma from n=1 to infity of n/2^n
A. Let $\ell(x):=\textstyle\sum\nolimits_{n=0}^{\infty}x^{ n}$, and show that $\ell(x)=1/(1-x)$, then calculate $\ell^{\prime}(x)$ for $|x|<1$.
B.1. Calculate $x\ell^{\prime}(x)$ for $|x|<1$.
B.2. Check $\ell^{\prime}(1/2)/2$.