integral test

Consider a sequence (an)={a0,a1,a2,a3,} and given M consider any monotonically nonincreasing function f:[M,+) which extends the sequence, i.e.

f(n)=an  nM

An example is

an=2n    f(x)=2x

(the former being the sequence {0,2,4,6,8,} and the later the doubling function for any real number.

We are interested on finding out when the summation



The integral testMathworldPlanetmath states the following.

The series


converges if and only if the integral


is finite.

Title integral test
Canonical name IntegralTest
Date of creation 2013-03-22 12:27:12
Last modified on 2013-03-22 12:27:12
Owner drini (3)
Last modified by drini (3)
Numerical id 20
Author drini (3)
Entry type Theorem
Classification msc 40A05
Related topic Function
Related topic Sequence
Related topic Limit