Can't resist mentioning my personal favorite expansion of a sqrt: 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

Can't resist mentioning my personal favorite expansion of a sqrt: 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 http://www.math.chalmers.se/~wastlund/coinFlip.pdf]