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Math Help - Help with a series

  1. #1
    Newbie
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    Help with a series

    I have the series (from 1 to infinity) of (1-(1/e^n))^n. I can't seem to find a test to help me establish convergence or divergence.

    Thanks for your help!

    Bret
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  2. #2
    Senior Member
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    What is the limit at infinity for (1-(1/e^n))^n?
    If it is not zero, then it diverges.
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  3. #3
    Member Pranas's Avatar
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    \[\mathop {\lim }\limits_{n \to \infty } {(1 - \frac{1}{{{e^n}}})^n} = \mathop {\lim }\limits_{n \to \infty } {e^{\ln (1 - \frac{1}{{{e^n}}}) \cdot n}} = {e^{\mathop {\lim }\limits_{n \to \infty } \frac{{ - {n^2}}}{{{e^n} - 1}}}} = {e^{\mathop {\lim }\limits_{n \to \infty } \frac{{ - 2}}{{{e^n}}}}} = 1\]
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  4. #4
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    Thanks everyone. I get really embarassed when I forget basic things. Cool explanation Pranas. Thanks also snowtea.
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