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Math Help - a problem about series

  1. #1
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    a problem about series

    i tried... i can't get tackle with this problem no matter how hard i try. please help me.

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  2. #2
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    Opalg's Avatar
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    Re: a problem about series

    It looks to me very much as though this series diverges. In fact, a bit of work with a pocket calculator suggests that e - \bigl(1+\tfrac1n\bigr)^n > \tfrac1n whenever n\geqslant3. More precisely, I'm finding that n\Bigl(e - \bigl(1+\tfrac1n\bigr)^n\Bigr) converges to a limit approximately 1.36 as n\to\infty.
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  3. #3
    Super Member girdav's Avatar
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    Re: a problem about series

    The series has non-negative terms, and e-\left(1+\frac 1n\right)^n\sim\frac e{2n} hence the series diverges, hence the sum is +\infty.
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