# Math Help - Using the ratio test to show a convergent series

1. ## Using the ratio test to show a convergent series

I'm trying to prove

is convergent.

I know I need to do the ratio test but I am lost after I do the (a_n +1) / (a_n) stage. I've watched a few vidoes on using the ratio test, but nothing in the above format, please help

2. ## Re: Using the ratio test to show a convergent series

Originally Posted by jennybee
I'm trying to prove
is convergent.
I know I need to do the ratio test but I am lost after I do the (a_n +1) / (a_n) stage. I've watched a few vidoes on using the ratio test.
$\frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}$

3. ## Re: Using the ratio test to show a convergent series

Originally Posted by Plato
$\frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}$
Thank you. Can this cancel down before I find the limit?