sqrt(1-x) = 1- \sum_n C(n)/2^(2n+1) x^(n+1)
where x is in (0,1) and C(n)=binomial(2n,n)/(n+1) is the n'th catalan number.
[Learned this from http://www.math.chalmers.se/~wastlund/coinFlip.pdf]