determining series convergence

Consider a series Σan. To determine whether Σan converges or diverges, several tests are available. There is no precise rule indicating which of test to use with a given series. The more obvious approaches are collected below.

The root test and the ratio test are direct applications of the comparison test to the geometric seriesMathworldPlanetmath with terms (|an|)1/n and an+1an, respectively.

For a paper about tests for convergence, please see article.

Title determining series convergence
Canonical name DeterminingSeriesConvergence
Date of creation 2013-03-22 13:24:45
Last modified on 2013-03-22 13:24:45
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 16
Author CWoo (3771)
Entry type Topic
Classification msc 40A05
Related topic ThenA_kto0IfSum_k1inftyA_kConverges
Related topic LimitComparisonTest
Related topic AbsoluteConvergence
Related topic InfiniteProductOfSums1a_i