The series converges

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

Problem

The series ∑k=2∞(−1) kln⁡kk2\displaystyle\sum_{k=2}^{\infty} (-1)^{\,k}\dfrac{\ln k}{k^{2}} converges. Using the first four nonzero terms to approximate its sum, which of the following is the largest possible magnitude of the error of this approximation? (a) 0.0640.064 (b) 0.0400.040 (c) 0.0500.050 (d) 0.0450.045

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