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Math Help - the sum to infinity

  1. #1
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    Question the sum to infinity

    For the following geometric serie, find the range of values of x for which the sum to infinity of the serie exist.
    1 + \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} + ...
    Please help me with that problem.
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let S_n=1+\frac{1}{x}+\frac{1}{x^2}+\ldots+\frac{1}{x^  {n-1}}

    Then S_n=\frac{x}{1-x}\left[\left(\frac{1}{x}\right)^n-1\right]

    S_n converges if \left|\frac{1}{x}\right|<1\Rightarrow |x|>1\Rightarrow x\in(-\infty,-1)\cup(1,\infty)
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