1. ## Just for Fun

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

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

2. The answer is $\displaystyle \sqrt \pi$!

The solution is easy : Gamma duplication formula!

3. Good job!

4. Thank you for the problem!

5. 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.

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

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