(this is called the generating function, or generating series, for the complete homogeneous symmetric polynomials). Here each fraction in the final expression is the usual way to represent the formal geometric series that is a factor in the middle expression. The identity can be justified by considering how the product of those geometric series is formed: each factor in the product is obtained by multiplying together one term chosen from each geometric series, and every monomial in the variables is obtained for exactly one such choice of terms, and comes multiplied by a power of equal to the degree of the monomial.