Determine the value of the series .

MATHEMATICS · Single correct · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

Determine the value of the series ∑k=2∞1k(k−1)\displaystyle\sum_{k=2}^{\infty}\frac{1}{k(k-1)}. (a) 00 (b) 11 (c) ln⁡2\ln 2 (d) It diverges without bound.

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