# Given

Both $y$ and $n$ are series. For all n... (sorry I used the same letter twice in different contexts...)

$$y*n = 1 - n*n$$

$$0 < y_n < 1$$

$$(n*0 * n*1 * ... * n*{n+1}) * (y*0/n*0 + y*1/n*1 + ... + y*{n+1}/n*{n+1}) > (n*0 * n*1 * ... * n*n) * (y*0/n*0 + y*1/n*1 + ... + y*n/n*n)$$

# Prove

That $(n*0 * n*1 * ... * n*{n+1}) * (y*0/n*0 + y*1/n*1 + ... + y*{n+1}/n*{n+1}) > (n*0 * n*1 * ... * n*n) * (y*0/n*0 + y*1/n*1 + ... + y*n/n*n)$ is true when $(n*0 * n*1 * ... * n_n) > 1$.