On page 67, "According to the binomial theorem," ...
What follows on the right hand side, I'm not sure where that came from.
According wikipedia: (1+x)^n = \sum_{k=0}^n {n \choose k}x^k. If you plug in 1/2 for n, you get a sum from n=0 to n=1/2, not n=0 to n=infinity as in the paper. So, this is confusing :)