The series converges to

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

Problem

The series ∑n=1∞4n(n+2)\displaystyle\sum_{n=1}^{\infty}\dfrac{4}{n(n+2)} converges to S=3S=3. What is the least positive integer NN for which ∣S−SN∣<0.01|S-S_N|<0.01? (a) 400400 (b) 399399 (c) 398398 (d) 199199

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