Just for Fun

**chiph588@** · December 17th 2009, 01:03 PM

This problem is just for fun, meant as a challenge.

Calculate $\lim_{n \to \infty} \frac{2^{2n-1}((n-1)!)^2 \sqrt{n}}{(2n-1)!}$ .

**Bruno J.** · December 17th 2009, 07:11 PM

The answer is $\sqrt \pi$ !

The solution is easy : Gamma duplication formula!

**chiph588@** · December 17th 2009, 07:29 PM

Good job!

**Bruno J.** · December 17th 2009, 07:37 PM

Thank you for the problem!

**chiph588@** · December 17th 2009, 07:41 PM

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.

**Bruno J.** · December 17th 2009, 08:31 PM

I don't know, I just thought of it right away. I think $2^{2n-1}$ gave it away!

**NonCommAlg** · December 19th 2009, 01:46 AM

i'm sure you guys know that applying Strling's formula will make the problem very straightforward.

Thread: Just for Fun