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Basic Comparison Test

  1. Nov 1, 2011 #1
    [tex]\sum_{n=1}^\infty \frac{1}{n!}[/tex]

    I understand what n! means, but I have no clue what to compare this to. It is obvious to me that the sum converges, but I'm not sure how to prove it. I assume I would compare it to a p-series but I need help. Thanks!
  2. jcsd
  3. Nov 1, 2011 #2
    Compare it to [itex]1/n^2[/itex]...
  4. Nov 1, 2011 #3
    lol, I just realized how simple this is. my bad.
  5. Nov 1, 2011 #4
    Sorry, one more.

    [tex]\sum_{n=1}^\infty \frac{2^n}{n^2}[/tex]

    What would I compare this to?

    I can clearly see that it diverges since numerator is waaaay bigger but I don't know how to prove it.
  6. Nov 1, 2011 #5
    Calculate the limit of the terms and show that the limit isn't 0.
  7. Nov 1, 2011 #6
    Sorry I didn't specify. I understand how to use the limit test. For this problem I am supposed to compare it to something. Thanks for putting up with my questions :).

    edit: since 2^n is soo much bigger then n^2 can I compare it to 2^n?
  8. Nov 1, 2011 #7
    Maybe the harmonic series??

    It's a stupid exercise anyway if you're not allowed to do the limit test.
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