For which of the following series is the th-term test inconclusive

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

Problem

For which of the following series is the nnth-term test inconclusive, so that another convergence test is required? (a) ∑n=1∞3nn+2\displaystyle\sum_{n=1}^{\infty}\frac{3n}{n+2} (b) ∑n=2∞1n(ln⁡n)2\displaystyle\sum_{n=2}^{\infty}\frac{1}{n(\ln n)^{2}} (c) ∑n=1∞(−1)n(n+5)n\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n}(n+5)}{n} (d) ∑n=1∞ln⁡nln⁡(n+1)\displaystyle\sum_{n=1}^{\infty}\frac{\ln n}{\ln(n+1)}

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