- #1

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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!

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- Thread starter PCSL
- Start date

- #1

- 146

- 0

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

- 22,129

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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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[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

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

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