Explain, in one to two sentences, why the harmonic series diverges even though…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Explain, in one to two sentences, why the harmonic series ∑n=1∞1n\displaystyle \sum_{n=1}^{\infty} \frac{1}{n} diverges even though lim⁡n→∞1n=0\displaystyle \lim_{n\to\infty} \frac{1}{n}=0.

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