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Math Help - test for the series for convergence or divergence 3

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    test for the series for convergence or divergence 3

    determine if series is convergent or divergent
    the sum from 1 to infinity of (-1)^n(2^(1/n))
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by twilightstr View Post
    determine if series is convergent or divergent
    the sum from 1 to infinity of (-1)^n(2^(1/n))
    Its somewhat similar to your other problem here.

    Whenever you have a \left(-1\right)^n term, you should always first start off with the alternating series test.

    The absolute value leaves us with 2^{\frac1n}

    Since 2^{\frac1n}>2^{\frac1{n+1}}, we need to see if \lim\left|s_n\right|=0. However, \lim\left|s_n\right|=\lim 2^{\frac1n}=1\neq0.

    Thus, it diverges.
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