Thread: Using Limit Comparison test

The problem I am giving is the series from 0 to infinity of 1/n!. It is an odd problem with answer given in back of book and states for n>3 (1/n^2)>(1/n!)>0. So the original series converges by comparison w/convergent p-series of (1/n^2).

Can some one tell me HOW they came up with 1/n^2 for comparison for 1/n!?

It is a standard problem to use induction to prove: if n>3 then (n!)>2^n.