# Finding a differential function for a series

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• 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 $f'(x)$.

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

I'm not sure I entirely understand this question or how to start.
• October 28th 2012, 08:20 AM
JJacquelin
Re: Finding a differential function for a series
to start, compute f '(x) : You just have to derivate the general term of the series.