Series convergence of 1/n! direct comparison -- difficult proof! Direct comparison sum(1/n!) proof.

Series convergence of 1/n! direct comparison sum(1/n!) approach: we compare to the convergent p-series 1/n^2. This requires showing that n! greater than n^2 when n is sufficiently large, which is a tricky proof because direct comparison with factorials is not simple. In the long run, you're better off using the ratio test in a convergence proof with factorials, but using direct comparison in the convergence with factorials proof here is instructive.

[random_sam]

you could have done it in an easier way using induction over n.