Which of the following infinite series diverges?

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

Problem

Which of the following infinite series diverges? (a) ∑n=1∞1n2\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{2}} (b) ∑n=1∞1n4/3\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{4/3}} (c) ∑n=1∞1n\displaystyle \sum_{n=1}^{\infty}\frac{1}{\sqrt{n}} (d) ∑n=1∞1n5/2\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^{5/2}}

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