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

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

Find a power series representation for the following function:

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

Here is how I started this:

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

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

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!!

2. Originally Posted by mollymcf2009
Find a power series representation for the following function:

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

Here is how I started this:

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

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

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 $\displaystyle \sum (-1)^n x^n$