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Thinning Out the Harmonic Series

by G. Hossein Behforooz (Syracuse University)

This article originally appeared in:
Mathematics Magazine
October, 1995

Subject classification(s): Series
Applicable Course(s): 3.2 Mainstream Calculus II | 4.11 Advanced Calc I, II, & Real Analysis

The subseries of the harmonic series, \(\sum_{n=1}^{\infty} \frac{1}{n}\), which consists of all terms with one or more nines in the digits of \(n\), is a divergent series.

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Capsule Course Topic(s):
Sequences and Series | Special Series: Harmonic Series
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