Integral Test
Related Topics:
More Lessons for Calculus
Math Worksheets
Suppose f is a continuous, positive, decreasing function on
and let an = f(n).
Then the series
is convergent if and only if the improper integral 
is convergent.
Integral Test - Basic Idea
Using the Integral Test for Series
You can use the free Mathway calculator and problem solver 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.
More Lessons for Calculus
Math Worksheets
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.Suppose f is a continuous, positive, decreasing function on
and let an = f(n).Then the series
is convergent if and only if the improper integral is convergent.
If is convergent then is convergent.
If is divergent then is divergent.
Example:
Test the series 
for convergence or divergence.
Solution:
The function 
is continuous, positive, decreasing function on [1,∞) so we use the Integral Test:
Since 
is a convergent integral and so, by the Integral test, the series is convergent.
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 calculator and problem solver 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.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
