More Lessons for Calculus
What is the The Integral Test?
The Integral Test enables us to determine whether a series is convergent or divergent without explicitly finding its sum.
is a continuous, positive, decreasing function on
and let an
). Then the series
is convergent if and only if the improper integral
If is convergent then is convergent.
If is divergent then is divergent.
Test the series for convergence or divergence.
The function is continuous, positive, decreasing function on so we use the Integral Test:
Since is a convergent integral and so, by the Integral test, the series is convergent.
Integral Test - Basic Idea
Using the Integral Test for Series
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.