Question

Does this sequence converge or diverge? Take the limit---
(n!)/(n + 1)
n= 0 to infinity

Answer 1

n! always ... ALWAYS, controls the stage

when n is very large, this is approximately equivalent to n!

Answer 2

do a ratio test

Answer 3

or simplicity\[\frac{\frac{n*(n-1)!}{n}}{\frac{n}{n}+\frac{1}{n}}\]

\[\frac{(n-1)!}{1+\frac{1}{n}}\]

\[\frac{(\infty-1)!}{1+\frac{1}{\infty}}=\infty\]