A "Harmonic" Series (Solved)

Summary: The problem is to show that $\sum_{n=1}^{\infty} (\log 3 - (H_{3n} - H_n))/n = \frac{5 \pi^2}{36} - \frac{3 \ln^2 3}{4}$, and prove or disprove a conjecture concerning the family of series in which the summand is $(\log k - (H_{kn}-H_n)/n$.

Classification: Primary, Classical Analysis; Secondary, Sequences and Series

Ovidiu Furdui
Department of Mathematics
Western Michigan University
Kalamazoo, MI 49008
Email 1: o0furdui@wmich.edu
Email 2: ofurdui@yahoo.com

Omran Kouba
Higher Institute for Applied Sciences and Technology
P. O. Box 31983
Damascus, Syria
e-mail: omran_kouba@hiast.edu.sy

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