10-seconds challenge-3

Calculus Level 2

$\Large {\dfrac{1}{\pi} e^{2 \ln\left(2\Gamma\left(\frac{3}{2}\right)\right)}} = \ ? \$

1 solution

Yash Dev Lamba
Mar 6, 2016

It is quite difficult to solve it in 10 sec but it is a challenge so we have to ...

$\Gamma(\frac{3}{2})$ = $\Gamma(1+\frac{1}{2})$ $= \frac{1}{2}$ $\Gamma(\frac{1}{2})$ $= \frac{\sqrt{\pi}}{2}$

$\frac{1}{\pi} e^{2ln(\sqrt{\pi})} = \frac{1}{\pi} e^{ln(\pi)}=\pi \times \frac{1}{\pi} =\boxed{1}$

I doubt that we could do this in 10 seconds :P

I think 30 seconds would suffice.

Mehul Arora - 5 years, 3 months ago

I know it is difficult to solve it in 10 sec that 's why it is a challenge

Yash Dev Lamba - 5 years, 3 months ago

I solved it in 15secs

Aareyan Manzoor - 5 years, 3 months ago

@Aareyan Manzoor – Okay, never mind :P

Still, 10 seconds IS less.

Mehul Arora - 5 years, 3 months ago