  Summation by parts is used to find the sum of a finite series of generalized
harmonic numbers involving a specific polynomial or rational function. The
Euler-Maclaurin formula for sums of powers is used to find the sums of some
finite series of generalized harmonic numbers involving nonnegative integer
powers, which can be used to evaluate the sums of the finite series of
generalized harmonic numbers involving polynomials. Many examples and a
computer program are provided.
