Calculus 2: The Integral Test (Section 11.3) | Math with Professor V

Introduction to the integral test, necessary conditions to apply it, discussion of p-series; various examples applying integral test.
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[@mathwithprofessorv]

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[@akshitmonga478]

For the last problem covered can we not use the divergence test there as we take the limit as n approaches infinity? The exponent of e would approach 0 making the numerator a constant and the denominator would approach infinity making the limit = to 0, meaning it’s convergent right.

[@mathwithprofessorv]

No, the Test for Divergence can only be used to show the DIVERGENCE of a series. If the terms approach zero then you have no info, the series may converge or diverge.

[@akshitmonga478]

@@mathwithprofessorv ahhh I see thank you

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[@gtsang5714]

For example 3b (18:51), can't you just find the 'r' like you did last lesson, section 11.2, and see if it's greater or less than 1? Also for example 4 (26:27), can't you use the P-series?

[@mathwithprofessorv]

No and no. 3b is not a geometric series, so finding r does not apply (there is no r). Example 4 is not a p-series, look at the numerator.

[@gtsang5714]

@@mathwithprofessorv I see, thank you. So in order to use the P-series the numerator must be a 1.
Your videos are super helpful in comparison to my professor who only cover less than half of each section and gives us homework after.

[@mathwithprofessorv]

@@gtsang5714 I’m so happy my videos are helpful to you! If you watch the video on Comparison Test and Limit Comparison Test you will see how you can use p-series as a basis for determining if a series converges or diverges. But if you’re not using one of those tests then yes, the numerator needs to be a constant.