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Math Help - Series Divergence/Convergence

  1. #1
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    Series Divergence/Convergence

    Need some help with this question

    does the series

    Sum of \frac{2^n}{n^2} from n=1 to infinity

    i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..
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  2. #2
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    Quote Originally Posted by Kevlar View Post
    Sum of \frac{2^n}{n^2} from n=1 to infinity
    i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..
    You made a mistake.
    Ratio: \frac{a_{n+1}}{a_n}.
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  3. #3
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    ahhh yeh i got it now i got 2 which is >1 therefore divergent
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  4. #4
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    As a matter of fact, for some "n" will get that the numerator is bigger than the denominator, hence the divergence is obvious.
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  5. #5
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    Quote Originally Posted by Kevlar View Post
    Need some help with this question

    does the series

    Sum of \frac{2^n}{n^2} from n=1 to infinity

    i've tried ratio test method and end up with 1/2 which says the series converges but this series apparently diverges..

    Excause me, Do you know the nth term test ?
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