MHB Do These Infinite Series Converge?

[Tebow15]

Test these for convergence.

1.
infinity
E...n!/(n! + 3^n)
n = 0

2.
infinity
E...(n - (1/n))^-n
n = 1

Btw, E means sum.

Which tests should I use to solve these?

 

[chisigma]

1. $\displaystyle \sum_{n=0}^{\infty} \frac{n!}{n! + 3^n}$

What is $\displaystyle \lim_{n \rightarrow \infty} \frac{n!}{n! + 3^n}$?...

Kind regards

$\chi$ $\sigma$

 

[alyafey22]

2.
infinity
E...(n - (1/n))^-n
n = 1

This sum is undefined at n=1 !