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Math Help - Series 1/(2^(sqrt(n))

  1. #1
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    Series 1/(2^(sqrt(n))

    sum (1/(2^(sqrt(n)))) from 1 to infinity - Wolfram|Alpha

    I need to prove that this series converges. Thanks
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  2. #2
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    Re: Series 1/(2^(sqrt(n))

    This is a special case of the limit comparison test.

    If each of \sum {{a_n}} \;\& \;\sum {{b_n}} is a series of positive terms and \sum {{b_n}} converges and if {\lim _{n \to \infty }}\frac{{{a_n}}}{{{b_n}}} = 0 then \sum {{a_n}} also converges.
    Thanks from topsquark
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    Re: Series 1/(2^(sqrt(n))

    I know that but I have a problem finding series to compare to.
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    Re: Series 1/(2^(sqrt(n))

    Quote Originally Posted by kicma View Post
    I know that but I have a problem finding series to compare to.
    HINT: {\lim _{n \to \infty }}\frac{{{n^2}}}{{{2^{\sqrt n }}}} = ?
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  5. #5
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    Re: Series 1/(2^(sqrt(n))

    Thanks, I got it.
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