We present an algorithm for proving certain families of polynomial
in which the number of variables appears as a parameter.
Typically, indefinite sums and products (possibly nested) are used for
defining such polynomial identities, but in principle the definition
of the problem may be given in terms of arbitrary polynomial
recurrences (possibly nonlinear).
An implementation of our algorithm in Mathematica was able to verify
identities appearing in textbooks, which, to our knowledge, were
previously not accessible by any symbolic method.
A collection of examples is included in the papers.