# How do you use the Ratio Test on the series #sum_(n=1)^oon^n/(n!)# ?

##### 1 Answer

Recall: **The Definition of Number #e#**

(Note: This can be derived suing l'Hopital's Rule as well.)

Now, let us examine the convergence of the posted series.

By the Ratio Test ,

by cancelling out common factors,

by simplifying a bit further,

Hence, the series diverges.

I hope that this was helpful.