MAT136H1 Study Guide - Midterm Guide: Integral Test For Convergence, Improper Integral
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11.3 Infinite Sequences & Series
Integral Test & Sum Estimates
Question #2 (Medium): Integral Test for Convergent Series
For function is continuous, positive, and decreasing over , let
is convergent if its improper integral
If the improper integral
is divergent, then the series
is also divergent
Use the integral test to determine if the series is convergent or divergent.
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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