Determine if the series converges or diverges

Question

∞
∑ (n!/3ⁿ)
n=0

Answer 1

The series diverges.

When n >4, each term in

∞
∑ (n!/3n) >  ∑1/n
n=0
∑1/n is a well known divergent series. Hence by the comparison test, the above series diverges.