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Math Help - Ratio & root test question

  1. #1
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    Ratio & root test question

    Is it true that if a series converges according to the ratio/root test, then the series converges to zero?
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  2. #2
    Senior Member
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    In general, no. Consider the series

    1=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots

    where both the ratio \frac{a_{k+1}}{a_k} and the root (a_k)^{1/k} converge to 1/2 as k\rightarrow \infty.
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