Need help determining whether this series converges or not:
$$\sum_{1}^{\infty}\frac{ 2n! }{ n!^2 }$$
My thoughts are this is a candidate for ratio test, so I rewrote it
$$\left| \frac{ 2(n+1)! }{ ((n+1)!)^2 } \right| * \left| \frac{ n!^2 }{ 2n! } \right|$$
But I do not know how to simplify this expression.

Question

Need help determining whether this series converges or not: 
$$\sum_{1}^{\infty}\frac{ 2n! }{ n!^2 }$$
   My thoughts are this is a candidate for ratio test, so I rewrote it 
$$\left| \frac{ 2(n+1)! }{ ((n+1)!)^2 } \right| * \left| \frac{ n!^2 }{ 2n! } \right|$$
  But I do not know how to simplify this expression.

turingtest · Answer

$$\frac{(n+1)!}{n!}=n+1$$did you know that?

anonymous · Answer

2(n+1)/2(n+1)

turingtest · Answer

don't drop the square on the other one...

anonymous · Answer

Wait thats wrong again, sorry, doing this in my head.

anonymous · Answer

2(n+1)/2(n+1)^2

turingtest · Answer

yes, and the 2's cancel...

anonymous · Answer

1/(n+1)  so by the ratio test, if L<1 it converges?

turingtest · Answer

correct :)

anonymous · Answer

Really appreciate you working with me! Thanks

turingtest · Answer

very welcome!