Which of the following series cannot be examined with an improper integral of a…

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

Problem

Which of the following series cannot be examined with an improper integral of a related function on any tail of the series because at least one required condition fails to hold? (a) ∑n=2∞1n ln⁡n\displaystyle \sum_{n=2}^{\infty} \dfrac{1}{n\,\ln n} (b) ∑n=3∞1n1/2\displaystyle \sum_{n=3}^{\infty} \dfrac{1}{n^{1/2}} (c) ∑n=1∞sin⁡nn\displaystyle \sum_{n=1}^{\infty} \dfrac{\sin n}{n} (d) ∑n=1∞nn2+1\displaystyle \sum_{n=1}^{\infty} \dfrac{n}{n^{2}+1}

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