# Limit of factorial

1. Apr 7, 2009

### Geekchick

1. The problem statement, all variables and given/known data
Determine the divergence or the convergence of the sequence. If it converges find its limit.

a$$_{n}$$ = ($$\frac{(n)!}{2n!+1}$$)

3. The attempt at a solution

I like to think of limits this way. First intuatively say why it should converge or diverge, then apply the intuation in a rigorous way. In this case both top and bottom are about the same thing so you would expect it to converge. How to say this in a formal manner? Use an inequality that will enable you to cancel the factorials and use the theorem that says if $0 \leq a_n \leq b_n$ for each n, then if b_n converges, so does a_n.