An algorithm which finds the definite sum of many series involving binomial coefficients b presented. The method examines the ratio of two consecutive terms of the series in an attempt to express the sum as an ordinary hypergeometric function. A closed form for the infinite sum may b* found by comparing the resulting function with known summation theorems. It may also be possible to identify ranges of the summation index for which summing to a finite upper limit is the same as summing to infinity.