Hey guys,

I'm trying to use the ratio test to find divergence/convergence, however I was never taught factorials in depth so I don't understand how they work.

I was given the question

\(\sum_{n=1}^{inf}\frac{3^nn!n!}{(2n)!}\)

The way that I did it the expression diverges because it goes to infinity but that's apparently wrong, so how would I be able to solve something like this?

bingby
Apr 18, 2017

#1
**0 **

I tried to simplify it and was getting the limit as n goes to infinity of 3(n+1)^2 divided by (2n+2)(2n+1). The numerator and denominator have the same degree of n so they cancel out and the limit as n goes to infinity reaches the constant 3. 3>1 so from my calculations it should still diverge but I am still wrong.

bingby
Apr 18, 2017