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Math Help - Test the series convergence

  1. #1
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    Test the series convergence

    this is a hard one
    I tried many times
    and I always failed
    here is it:

    \sum_{n=2}^{\infty} \frac{1}{ln^e \, (n)}
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  2. #2
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    Quote Originally Posted by TWiX View Post
    this is a hard one
    I tried many times
    and I always failed
    here is it:

    \sum_{n=2}^{\infty} \frac{1}{ln^e \, (n)}

    There always exists N_k\in\mathbb{N}\,\,\,s.t.\,\,\,n>N_k\Longrightarr  ow \ln^k(n)<n , no matter what k\in\mathbb{N} is, so...

    Tonio
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