Does the series ((n^n)/n!) converge?

[@mnek742]

Interesting solution! But it was completely unnecessary to use any test. The numerator of each term is n^n, the product of n multiplications of n. The denominator is n!, the product of the first n natural numbers. The numerator is much bigger than the denominator for all n>1, so each fraction is more than 1 for all n>1, so not only does the series not converge, the sequence doesn't converge either.

[@adhipadhikari4415]

You are absolutely correct! Just wanted to use the ratio test to prove this. Thanks for pointing this out. Will be extremely helpful for those who watch this vid.