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Math Help - Help with Power Series: Proof

  1. #1
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    Help with Power Series: Proof

    Prove that for -1<x<1

    1/(x+1) =

    infinite
    Σ [(-1)^n][x^n] = 1 - x + x^2 - x^3 + ...
    n=0

    ln(1+x) =

    infinite
    Σ [(x^n)(-1)^(n-1)]/n = x - (x^2)/2 + (x^3)/3 - (x^4)/4...
    n=0
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  2. #2
    MHF Contributor matheagle's Avatar
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    thats a geo

    {1\over 1+x}={1\over 1-(-x)}=\sum_{n=0}^{\infty}(-x)^n

    Next integrate AND do not forget the +C, which by setting x=0 becomes 0.

    AND your sum is wrong, you must start at n=1. You cannot divide by 0.
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  3. #3
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    thank you!
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by wyhwang7 View Post
    Prove that for -1<x<1
    infinite
    Σ [(x^n)(-1)^(n-1)]/n = x - (x^2)/2 + (x^3)/3 - (x^4)/4...
    n=0

    I hope your book does not start this sum at zero.
    It looks like 1 to me.
    You cannot divide by 0, anywhere.
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