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∞1n1.01\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^{1.01}} (b) ∑n=1∞1n\displaystyle \sum_{n=1}^{\infty} \frac{1}{n} (c) ∑n=1∞1n1.2\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^{1.2}} (d) ∑n=2∞1n(ln⁡n)2\displaystyle \sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{2}}

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