a series related to harmonic series

The series

n=11nnn=n=11n1+1n (1)

is divergent.  In fact, since for every positive integer n, one has  2n>n,  i.e.  nn<2, any of the series satisfies


Because the harmonic series and therefore also 112n diverges, the comparison testMathworldPlanetmath implies that the series (1) diverges.

Title a series related to harmonic series
Canonical name ASeriesRelatedToHarmonicSeries
Date of creation 2013-03-22 17:56:40
Last modified on 2013-03-22 17:56:40
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Example
Classification msc 40A05
Related topic PTest
Related topic RaabesCriteria