Identities for many and varied combinations of binomial coefficients abound. Indeed, because of the wide range of interrelationships it is possible that a great deal of mathematical effort has been wasted in proving essentially equivalent formulae. As well as proving identities these methods can be used to rule out closed form solutions (at least of the form assumed by them) for certain sums. In this article, various methods for producing formulae for partial row-sums of Pascal's triangle are explored and a novel way of picking out a particular term of a power series introduced. (Contains 1 table.)