Department

MathematicsCourse Code

MAT136H1Professor

allStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**1 pages of the document.**11.3 Infinite Sequences & Series

Integral Test & Sum Estimates

Question #2 (Medium): Integral Test for Convergent Series

Strategy

For function is continuous, positive, and decreasing over , let

The series

is convergent if its improper integral

is convergent

If the improper integral

is divergent, then the series

is also divergent

Sample Question

Use the integral test to determine if the series is convergent or divergent.

Solution

The series function

is continuous, positive, and decreasing over , so the

integral test can apply.

Then set up the improper integral:

Therefore, since the improper integral converges, the series also converges according to the integral test.

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