# Replace $$x$$ by $$1-x$$, right

Calculus Level 5

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

$I_n (k) = \int \limits_0^1 x^k (1-x)^{n-k} \text{d}x$

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

×