The Harmonic Series and the nth Term Test for Divergence

Details The Harmonic Series and the nth Term Test for Divergence The Harmonic Series and the nth Term Test for Divergence

2007-06-17

arxiv.org/abs/0706.2513v1

The American Mathematical Monthly, Vol. 107, No. 7, August-Septemeber 2000, p. 651

Mathematics

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Scientific paper

The divergence of the harmonic series is proved by direct comparison with a
series whose nth partial sum telescopes to the natural logarithm of n. The key
idea is to apply the classical inequality x>=log(1+x) (valid for x>-1) with
x=1/k and sum over k, 1<=k<=n-1.

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