limit comparison test

The following theorem is a powerful test for convergence of series.

Theorem 1 (Limit ).

Let n=0an and n=0bn be two series of positive numbers.

  1. 1.

    If the limit


    exists and L0 is a non-zero finite number, then both series n=0an and n=0bn converge or both diverge.

  2. 2.

    If L=0 and n=0bn converges then n=0an converges as well. If L=0 and n=0an diverges then n=0bn diverges as well.

  3. 3.

    Similarly, if the limit is infinite (“L=”) and n=0an converges then n=0bn converges as well. If L= and n=0bn diverges then n=0an diverges as well.

Title limit comparison testMathworldPlanetmath
Canonical name LimitComparisonTest
Date of creation 2013-03-22 15:01:31
Last modified on 2013-03-22 15:01:31
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Theorem
Classification msc 40-00
Related topic DeterminingSeriesConvergence
Related topic SequenceDeterminingConvergenceOfSeries