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=13⋅1n>0 |
Because ∑∞n=1131n (the harmonic series divided by 3) diverges, then also (2) diverges.
Title | examples using comparison test without limit |
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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 |