calculus problem help

Question

Find the limit of the sequence of partial sums whose general term is  .

	10
	0
	1
	Does not exist

I missed today's class, so help would be greatly appreciated

Answer 1

n! grows faster than 10ⁿ...after n=10, n! adds a factor bigger than 10 for each n,

i.e. lim as n->∞ of a_n=0.

This is not a formal argument, but it can be easily formalized if you need to do it.