The th partial sum of a series is

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

Problem

The nnth partial sum of a series is Sn=ln⁡(n+2)−ln⁡2\displaystyle S_n=\ln(n+2)-\ln 2. Which statement correctly describes the behavior of the series? (a) The series converges to ln⁡2\ln 2. (b) The series diverges because lim⁡n→∞Sn=+∞\displaystyle \lim_{n\to\infty}S_n = +\infty. (c) The series converges conditionally since the terms approach 00. (d) The series diverges to −∞-\infty because the logarithm becomes negative for large nn.

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