Basic Comparison Test

  • Thread starter PCSL
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  • #1
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[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!
 

Answers and Replies

  • #2
22,089
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Compare it to [itex]1/n^2[/itex]...
 
  • #3
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Compare it to [itex]1/n^2[/itex]...
lol, I just realized how simple this is. my bad.
 
  • #4
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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.
 
  • #5
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Calculate the limit of the terms and show that the limit isn't 0.
 
  • #6
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Calculate the limit of the terms and show that the limit isn't 0.
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?
 
  • #7
22,089
3,296
Maybe the harmonic series??

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

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