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Math Help - [SOLVED] Determine if the series converges

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    [SOLVED] Determine if the series converges

    the series is \frac{1}{e^{1/k}} with k=1 going to infinity
    do i use the divergence test and get my limit as 1 which means the series diverges?
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  2. #2
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    Quote Originally Posted by vinson24 View Post
    the series is \frac{1}{e^{1/k}} with k=1 going to infinity
    do i use the divergence test and get my limit as 1 which means the series diverges?

    If the series is \sum^\infty_{k=1}\frac{1}{e^{1/k}} , then \lim_{k\to\infty}\frac{1}{e^{1/k}}=\frac{1}{e^{\lim_{k\to\infty}1/k}}=\frac{1}{e^0}=1\neq 0 and thus the series can't converge.

    Tonio
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    thanks i wanted to make sure i picked the right test
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