Which of the following infinite series converges?

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

Problem

Which of the following infinite series converges? (a) ∑n=1∞1ln⁡ ⁣(n+1)\displaystyle\sum_{n=1}^{\infty}\frac{1}{\ln\!(n+1)} (b) ∑n=1∞1n\displaystyle\sum_{n=1}^{\infty}\frac{1}{n} (c) ∑n=1∞1n3/2\displaystyle\sum_{n=1}^{\infty}\frac{1}{n^{3/2}} (d) ∑n=1∞3n2n\displaystyle\sum_{n=1}^{\infty}\frac{3^{n}}{2^{n}}

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