Ramanujan-inspired series for 1/π involving harmonic numbers

Abstract By applying the derivative operator to the known identities from hypergeometric series or WZ pairs, we obtain seven series associated with harmonic numbers. Specifically, six of them are Ramanujan-like formulas for 1/π and the remaining one contains harmonic numbers of order 2. As conclusions, Sun's five conjectural series are proved. 2010 Mathematics Subject Classification. Primary 33D15; Secondary 05A15.