The series converges to

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The series ∑n=1∞1n(n+1)\displaystyle\sum_{n=1}^{\infty}\dfrac{1}{n(n+1)} converges to S=1S=1. What is the value of ∣S−S49∣|S-S_{49}|? (a) 0.02040.0204 (b) 0.040.04 (c) 0.020.02 (d) 0.00040.0004

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