  A simple proof of a new summation formula for a terminating r+3Fr+2(1)
hypergeometric series, representing an extension of Saalschutz's formula for a
3F2(1) series, is given for the case of r pairs of numeratorial and
denominatorial parameters differing by positive integers. Two applications of
this extended summation theorem are discussed. The first application extends
two identities given by Ramanujan and the second, which also employs a similar
extension of the Vandermonde-Chu summation theorem for the 2F1 series, extends
certain reduction formulas for the Kamp?e de F?eriet function of two variables
given by Exton and Cvijovi?c and Miller.
