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ERJAEE, G. (20)

Lecture 20

Department

MathematicsCourse Code

MATH 2BProfessor

ERJAEE, G.Lecture

20This

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MATH 2B - Lecture 19 - Integral Test

● For most of the series, we are not able to find , therefore we need other

techniques for convergence test

Example:

Determine whether the series

is convergent

Solution:

● Series

● Multiply by 1:

● Recall the definition of improper integral

● We can find every term in S on the curve

● We then treat each term as a rectangle, with height , and base “1”. If we use

right-endpoint rule, we can obtain a rectangle approximation. Comparing to the

area

, we know

○ Also we know that

● Therefore we know that the series

is convergent

● That’s the basic idea of integral test, where we relate the series to a certain

improper integral

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