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

  1. #1
    Senior Member mollymcf2009's Avatar
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    [SOLVED] manipulating power series ln(1+x)

    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!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    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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