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Math Help - How to find whether this series converges or diverges

  1. #1
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    How to find whether this series converges or diverges

    Problem: Determine whether the following series converges or diverges.

    n! / (n^n)

    I know that I need to find another function to compare it to, but I'm at a complete loss for one that will give me a finite limit (and easy to tell whether it is conv or div) or one that is always bigger and converges, or always smaller and diverges. Does anyone have any suggestions as to what I should use? Thank you.
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  2. #2
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    Quote Originally Posted by uberbandgeek6 View Post
    Problem: Determine whether the following series converges or diverges.

    n! / (n^n)

    I know that I need to find another function to compare it to, but I'm at a complete loss for one that will give me a finite limit (and easy to tell whether it is conv or div) or one that is always bigger and converges, or always smaller and diverges. Does anyone have any suggestions as to what I should use? Thank you.
    You call it a series so why not use the ratio test?

    \lim_{n\rightarrow\infty} \frac{(n+1)!}{(n+1)^{(n+1)}}\cdot \frac{n^n}{n!}
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  3. #3
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    Quote Originally Posted by artvandalay11 View Post
    You call it a series so why not use the ratio test?

    \lim_{n\rightarrow\infty} \frac{(n+1)!}{(n+1)^{(n+1)}}\cdot \frac{n^n}{n!}
    We haven't learned that yet in class, so I would probably get docked points for not using one of the strategies I listed above.
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