## 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

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**Ovidiu Furdui**

Department of Mathematics

Western Michigan University

Kalamazoo, MI 49008

Email 1: [email protected]

Email 2: [email protected]

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**Omran Kouba**

Higher Institute for Applied Sciences and Technology

P. O. Box 31983

Damascus, Syria

e-mail: [email protected]