Mathematics

Mathematics

Problem

Let S=∑n=2∞ln⁡nn2S=\displaystyle\sum_{n=2}^{\infty} \dfrac{\ln n}{n^{2}}. Which statement about SS is true? a) SS diverges since the terms behave like 1/n1/n for large nn.},{ b) SS converges conditionally but not absolutely. c) SS converges because ∫2∞ln⁡xx2 dx\displaystyle\int_{2}^{\infty}\dfrac{\ln x}{x^{2}}\,dx is finite. d) SS diverges because ∫2∞ln⁡xx2 dx\displaystyle\int_{2}^{\infty}\dfrac{\ln x}{x^{2}}\,dx is infinite.

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