- #1

MathewsMD

- 433

- 7

## Homework Statement

Determine if the following series is divergent or convergent:

## ∑_1^∞ \frac {(2)(4)(6)...(2n)}{n!} ##

**2. The attempt at a solution**

I understand this can be simplified to:

## ∑_1^∞ \frac {(2^n)(n!)}{n!} ##

This can easily be seen to be divergent.

But when I do ## lim_{n→∞}\frac {a_{n+1}}{a_{n}} = lim_{n→∞}\frac {1}{n} ## after simplifying. Does anyone know what I may be doing wrong or why this is not appropriate? Is there any restriction on when the ratio test can be used? Thank you! :)