Finding a differential function for a series

**MathIsOhSoHard** · October 28th 2012, 08:13 AM

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 $f'(x)$ .

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

I'm not sure I entirely understand this question or how to start.

**JJacquelin** · October 28th 2012, 08:20 AM

to start, compute f '(x) : You just have to derivate the general term of the series.

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