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Math Help - geometric series

  1. #1
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    geometric series

    find the sum for the infinite geometric series

    3-3/2+3/4-...



    1+1/3+1/9+...
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  2. #2
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    Hi !

    Quote Originally Posted by gumi View Post
    find the sum for the infinite geometric series

    3-3/2+3/4-...
    3-\frac 32+\frac 34+\dots=3 \left(1-\frac 12+\frac 1{2^2}-\dots\right)=3 \sum_{n=0}^\infty \left(-\frac 12\right)^n



    1+1/3+1/9+...
    =\sum_{n=0}^\infty \left(\frac 13\right)^n

    -----------------------

    If |x|<1, then \sum_{n=0}^\infty x^n=\frac{1}{1-x}

    In general, we have :

    \sum_{n=0}^N x^n=\frac{1-x^{N+1}}{1-x}
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