How do you use the Ratio Test on the series #sum_(n=1)^oon^n/(n!)# ?
Recall: The Definition of Number
(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.