2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104907An algebraic transformation of the DeTemple-Wang half-integer approximation to the harmonic series produces the general formula and error estimate for the Ramanujan expansion for the nth harmonic number.7 pages. Acknowledgements added. Many typos corrected. Parts of the proof rewrittenClassical Analysis and ODEs26D5, 33B15text