for any real number formula_31. When formula_34, the formula_31-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the formula_31-series converges for all formula_37 (in which case it is called the over-harmonic series) and diverges for all formula_38. If formula_37 then the sum of the formula_31-series is formula_41, i.e., the Riemann zeta function evaluated at formula_31.