  This paper describes a method to find a connection between combinatorial
identities and hypergeometric series with a number of examples. Combinatorial
identities can often be written as hypergeometric series with unit argument. In
a number of cases these hypergeometric series are balanced and can be reduced
to a simpler form. In this paper some combinatorial identities are proved using
this method assuming that the results in the tables of Prudnikov et al. [12]
are proven without using hypergeometric functions.
