Determine Limit of Factorial Sequence a_n

[Geekchick]

Homework Statement

Determine the divergence or the convergence of the sequence. If it converges find its limit.

a_{n} = (\frac{(n)!}{2n!+1})

The Attempt at a Solution

All I know about factorials is for example 4! = 1*2*3*4. So as far as limits go I'm clueless. please help!

 

[Focus]

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.