Replace xx by 1x 1-x , right

Calculus Level 5

For integers, n\displaystyle n and k\displaystyle k , related as 0kn;nN\displaystyle 0 \leq k \leq n ; n \in \mathbb{N}, a sequence is defined as follows:

In(k)=01xk(1x)nkdx I_n (k) = \int \limits_0^1 x^k (1-x)^{n-k} \text{d}x

Evaluate: k=02014kI2014(k)k=02014I2014(k) \displaystyle \frac{ \sum_{k=0}^{2014} k I_{2014} (k) }{ \sum_{k=0}^{2014} I_{2014} (k) }

×

Problem Loading...

Note Loading...

Set Loading...