Hello

two hard problems:

1) Find a series $\displaystyle \sum a_n$ involves factorial but the ratio testcan notdetermine its convergence, i.e. $\displaystyle \lim_{n\to\infty} \frac{a_{n+1}}{a_n}=1$

2) Useonlythe comparison test to show that $\displaystyle \sum_{n=1}^{\infty} \frac{1}{n!}$ converges provided that the series (which you will use in the comparison) satisfy the conditions of the integral test and its nth term is integrable.

Actually I tried many times.

but they are too hard to me

and this is not for my homework

Actually, we do not have homeworks in my college

and sorry for my bad english