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Math Help - Power series

  1. #1
    Member kezman's Avatar
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    Power series

    I need to prove this(not sure how to):

    \sum_{n=0}^{\infty}{{(-1)^n}{x^n}} = \frac{1}{1+x}
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by kezman View Post
    I need to prove this(not sure how to):

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

    Assuming that |x|<1 and noting that this is a geometric series, what can you conclude ?
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