It's Always e!

Calculus Level 4

limnnn2((n+1)(n+12)(n+122)(n+12n1))n=ek\lim_{n\to\infty} n^{-n^{2}} \left((n+1)\left(n+\frac{1}{2}\right)\left(n+\frac{1}{2^{2}}\right)\cdots\left(n+\frac{1}{2^{n-1}}\right)\right)^{n} = e^{k}

Find the value of kk.


Notation: e2.71828e \approx 2.71828 denotes the Euler's number.

×

Problem Loading...

Note Loading...

Set Loading...