# Basic Comparison Test

1. Nov 1, 2011

### PCSL

$$\sum_{n=1}^\infty \frac{1}{n!}$$

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. Nov 1, 2011

### micromass

Staff Emeritus
Compare it to $1/n^2$...

3. Nov 1, 2011

### PCSL

lol, I just realized how simple this is. my bad.

4. Nov 1, 2011

### PCSL

Sorry, one more.

$$\sum_{n=1}^\infty \frac{2^n}{n^2}$$

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. Nov 1, 2011

### micromass

Staff Emeritus
Calculate the limit of the terms and show that the limit isn't 0.

6. Nov 1, 2011

### PCSL

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. Nov 1, 2011

### micromass

Staff Emeritus
Maybe the harmonic series??

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