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Thread: Show that a series diverges. Please Help ASAP!

  1. April 30th 2008, 12:34 AM #1
    jgall
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    Show that a series diverges. Please Help ASAP!

    Show that the series diverges:

    SUMMATION from k=0 to infinity of [(k+1)/k]^k

    All help is greatly appreciated!!
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  2. April 30th 2008, 12:37 AM #2
    Isomorphism
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    Quote Originally Posted by jgall View Post
    Show that the series diverges:

    SUMMATION from k=0 to infinity of [(k+1)/k]^k

    All help is greatly appreciated!!

    \lim_{k \to \infty} a_k = \lim_{k \to \infty} \left(1 + \frac1{k}\right)^k = e \neq 0

    If a series \sum_{k \in \mathbb{N}} a_k is convergent then a_k \to 0 as k \to \infty, but here \lim_{k \to \infty} a_k \neq 0
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