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Midterm

11.3 Integral Test & Sum Estimate Question #4 (Medium)

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Department
Mathematics
Course Code
MAT136H1
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all

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11.3 Infinite Sequences & Series
Integral Test & Sum Estimates
Question #4 (Medium): Eligibility for Integral Test
Strategy
Integral test can be applies only for continuous series functions which is positive everywhere and
decreasing over 
If the series function fails in that criteria, then the integral test cannot be applied.
Sample Question
Explain why the integral test cannot be used to determine if the series is convergent.
 


Solution
Since the series function contains secant trigonometric function which is a reciprocal function and has
cyclical vertical asymptotes and is not positive everywhere but rotates between positive and negative all
throughout , nor is it decreasing over the interval but repeatedly increases and decreases,
therefore the integral test cannot be applied. It fails in all of the three conditions required for eligibility
of integral test.

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Description
11.3 Infinite Sequences & Series Integral Test & Sum Estimates Question #4 (Medium): Eligibility for Integral Test Strategy Integral test can be applies only for continuous series functions which is positive everywhere and decreasing over [ ) If the series function fails in that criteria, then the integral test cannot be applied. Sample Question Explain why the integral test cannot be used to determine if the series is convergent. ∑ S
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