Question

Does the series converge or diverge?
Summation of n!/5^n

Answer 1

i would say diverge
factorials grow much faster than exponential functions

Answer 2

if you evaluate sum even for only first 50 terms its already at like 3 X10^29

Answer 3

well, you can evaluate it using the ratio test, but I'm not sure how to do all of the steps :/

Answer 4

Yeah ratio test confirms divergence. In the ration test you have (n+1)!/5^(n+1) divided by original one. This breaks down to (n+1)/5. Take limit. It goes to infinity. Infinity>0 diverge