# Just for Fun

• December 17th 2009, 01:03 PM
chiph588@
Just for Fun
This problem is just for fun, meant as a challenge.

Calculate $\lim_{n \to \infty} \frac{2^{2n-1}((n-1)!)^2 \sqrt{n}}{(2n-1)!}$.
• December 17th 2009, 07:11 PM
Bruno J.
The answer is $\sqrt \pi$!

The solution is easy : Gamma duplication formula!
• December 17th 2009, 07:29 PM
chiph588@
Good job!
• December 17th 2009, 07:37 PM
Bruno J.
Thank you for the problem! (Cool)
• December 17th 2009, 07:41 PM
chiph588@
How did you come about your solution? I thought it would be harder because a lot cancels out so it doesn't resemble the duplication formula.
• December 17th 2009, 08:31 PM
Bruno J.
I don't know, I just thought of it right away. I think $2^{2n-1}$ gave it away!
• December 19th 2009, 01:46 AM
NonCommAlg
i'm sure you guys know that applying Strling's formula will make the problem very straightforward.