[SOLVED] manipulating power series ln(1+x)

**mollymcf2009** · April 9th 2009, 05:16 PM

Find a power series representation for the following function:

$f(x) = ln (1+x)$

Here is how I started this:

$f'(x) = \frac{1}{1+x}$

$\sum^{\infty}_{n=0} (-x)^n$

Then I started to integrate, but I didn't know if I should do a definite or indefinite integral. If definite, what limits? Or, is this just not a good way to approach this problem? lol
CAn someone get me straight here?
Thanks!!

**Jhevon** · April 9th 2009, 08:56 PM

Originally Posted by mollymcf2009

Find a power series representation for the following function:

$f(x) = ln (1+x)$

Here is how I started this:

$f'(x) = \frac{1}{1+x}$

$\sum^{\infty}_{n=0} (-x)^n$

Then I started to integrate, but I didn't know if I should do a definite or indefinite integral. If definite, what limits? Or, is this just not a good way to approach this problem? lol
CAn someone get me straight here?
Thanks!!

find the indefinite integral, without the + C though. note also, that you have $\sum (-1)^n x^n$

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