# Finding a differential function for a series

• October 28th 2012, 08:13 AM
MathIsOhSoHard
Finding a differential function for a series
Given:
$f(x)=\sum^{\infty}_{n=1}\frac{2^n}{n}x^n$
$x\in]-1,1[$

Find a differential equation $f'(x)$, such that when you insert $x$ in the equation, you get $f'(x)$.

$f(x)=\frac{2}{1-2x}$