Sum to Infinity of Reciprocal of n^2 by 2n Choose n

Proof
By Sum to Infinity of 2x^2n over n by 2n Choose n, for $0 < \size x < 1$:

Substituting $x = 0$ gives:
 * $0 = 0 + C$

so $C = 0$.

Hence:

Also see

 * Sum to Infinity of Reciprocal of n by 2n Choose n