Using Ratio Test to Decide Convergent/Divergent

[McAfee]

Homework Statement

The Attempt at a Solution

I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.

 

[SammyS]

Homework Statement

The Attempt at a Solution

I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.

Your limit is wrong, because your ratio is wrong.

$\displaystyle\frac{(n+2)!}{(n+3)!}=\frac{1}{n+3}$

 

[McAfee]

Your limit is wrong, because your ratio is wrong.

$\displaystyle\frac{(n+2)!}{(n+3)!}=\frac{1}{n+3}$

Wow. I haven't used factorials in a while and forgot how they were used. Now looking at the problem I get L=0. That tells me that the series converges absolutely.

Thanks a lot. There are so many things is math to remember when solving a problem.