examples using comparison test without limit


Do the following series converge?

n=11n2+n+1 (1)
n=1n3+n+1n4+n+1 (2)

The general of (1) may be estimated upwards:

0<1n2+n+1<1n2+0+0=1n2

Because  n=11n2 (an over-harmonic series) converges, then also (1) converges.

The general of (2) may be estimated downwards:

n3+n+1n4+n+1>n3+0+0n4+n4+n4=131n>0

Because n=1131n (the harmonic seriesMathworldPlanetmath divided by 3) diverges, then also (2) diverges.

Title examples using comparison test without limit
Canonical name ExamplesUsingComparisonTestWithoutLimit
Date of creation 2013-03-22 15:08:55
Last modified on 2013-03-22 15:08:55
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Example
Classification msc 40-00
Related topic PTest
Defines over-harmonic series