Sequence promblem (show work)?

Question

Determine whether the sequence converges or diverges. If it converges, find the limit. If it diverges, enter NONE.

A(n)=(-8^n)/(n!)

Answer 1

After the eighth term, the sequence is monotonicly increasing. Moreover the terms are bounded above by 0 (since all terms are negative). That proves the sequence converges.

To prove that the limit is 0, use the definition of limit. If e > 0, show how to choose N so that if n > N, then -e < (-8^n)/n! < 0.

Answer 2

Do you know the ratio test?

Answer 3

woah that went over my head