# Using the ratio test to show a convergent series

• Mar 12th 2013, 01:31 PM
jennybee
Using the ratio test to show a convergent series
I'm trying to prove

Attachment 27502 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 (Crying)
• Mar 12th 2013, 01:42 PM
Plato
Re: Using the ratio test to show a convergent series
Quote:

Originally Posted by jennybee
I'm trying to prove
Attachment 27502 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.

$\displaystyle \frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}$
• Mar 12th 2013, 01:48 PM
jennybee
Re: Using the ratio test to show a convergent series
Quote:

Originally Posted by Plato
$\displaystyle \frac{a_{n+1}}{a_n}=\frac{(2n+7)^2}{(2n+5)^2}\cdot \frac{2^{n+1}}{2^n}\cdot\frac{n!}{(n+1)!}$

Thank you. Can this cancel down before I find the limit?