integral test
Consider a sequence and given consider any monotonically nonincreasing function which extends the sequence, i.e.
An example is
(the former being the sequence and the later the doubling function for any real number.
The integral test 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 |