Stolz-Cesaro theorem

Let (an)n1 and (bn)n1 be two sequences of real numbers. If bn is positive, strictly increasingPlanetmathPlanetmath and unboundedPlanetmathPlanetmath and the following limit exists:


Then the limit:


also exists and it is equal to l.

Remark. This theorem is also valid if an and bn are monotoneMathworldPlanetmath, tending to 0.

Title Stolz-Cesaro theorem
Canonical name StolzCesaroTheorem
Date of creation 2013-03-22 13:17:16
Last modified on 2013-03-22 13:17:16
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 9
Author CWoo (3771)
Entry type Theorem
Classification msc 40A05
Related topic CesaroMean
Related topic ExampleUsingStolzCesaroTheorem
Related topic KroneckersLemma