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Math Help - Convergence

  1. #1
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    Convergence

    Find all x for which this series converges: from n=0 to infinity, the summation of ((-1)^n)(x)^n/(4)^n?
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  2. #2
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    Quote Originally Posted by chaddy View Post
    Find all x for which this series converges: from n=0 to infinity, the summation of ((-1)^n)(x)^n/(4)^n?
    \sum_{n=0}^{\infty} (-1)^n \left( \frac{x}{4} \right)^n will converge (by the alternating series test) if \left| \frac{x}{4} \right|^n \rightarrow 0 as n \rightarrow \infty .....
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