For the alternating series

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

Problem

For the alternating series S=∑n=1∞(−1)n−1ln⁡nn\displaystyle S=\sum_{n=1}^{\infty} (-1)^{n-1}\dfrac{\ln n}{n}, the alternating series error bound can be applied only after the term magnitudes form a decreasing sequence. What is the smallest positive integer NN such that ln⁡nn\dfrac{\ln n}{n} is decreasing for every n≥Nn\ge N? (a) N=2N=2 (b) N=3N=3 (c) N=4N=4 (d) N=6N=6

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