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By applying the derivative operator to the known identities fromhypergeometric series or WZ pairs, we obtain seven series associated withharmonic numbers. Specifically, six of them are Ramanujan-like formulas for$1/\pi$ and the remaining onecontains harmonic numbers of order $2$. Asconclusions, Sun's five conjectural series are proved.

Ramanujan-inspired series for $1/\pi$ involving harmonic numbers