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anonymous

  • 4 years ago

Does the series: \sum_{n=2}^{\infty} n/ln (n) converge or diverge? What test do I use?

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  1. nenadmatematika
    • 4 years ago
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    well, you can remember that lim(n/lnn) is infinity when n goes to infinity so the series diverges

  2. anonymous
    • 4 years ago
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    \[\sum_{n=2}^{\infty} \frac{n}{\ln n} diverges\ since\ for\ a_{n} = \frac{n}{\ln n} \ we\ have \lim_{n \rightarrow \infty} \ a_{n} =\lim_{n \rightarrow \infty} \frac{1}{\frac{1}{n}} \rightarrow \infty\]

  3. nenadmatematika
    • 4 years ago
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    that's correct :D the good thing to know is if lim of an doesn't go to zero when n goes to infinity that's sufficient to conclude that your sum diverges....

  4. anonymous
    • 4 years ago
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    Thanks, your hint helped a lot.

  5. nenadmatematika
    • 4 years ago
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    you're welcome :D

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