2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/103832We obtain best possible upper and lower bounds for the Lodge-Ramanujan and DeTemple-Wang approximations to the nth Harmonic Number7 pages. Typos corrected. Several improvements in the exposition. Considerable strengthening of theorem 3 on the DeTemple-Wang approximation. Updated references, thanks to Dr. Feng QiClassical Analysis and ODEs26D15text