examples for limit comparison test

Example 1.

Does the following series converge?


The series is similar to n=11/n2 which converges (use p-test, for example). Next we compute the limit:


Therefore, since 10, by the Limit Comparison TestMathworldPlanetmath (with an=1/(n2+n+1) and bn=1/n2), the series converges.

Example 2.

Does the following series converge?


If we “forget” about the lower order terms of n:


and n=11/n is the harmonic seriesMathworldPlanetmath which diverges (by the p-test). Thus, we take bn=1/n and compute:


Therefore the series diverges like the harmonic does.

Title examples for limit comparison test
Canonical name ExamplesForLimitComparisonTest
Date of creation 2013-03-22 15:08:48
Last modified on 2013-03-22 15:08:48
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Example
Classification msc 40-00