naivlingr
2021-02-09
Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
tabuordy
Skilled2021-02-10Added 90 answers
Given: The series
To determine: The convergence and divergence of the given series by Integral test.
Explanation:
Integral Test: Let f(x) be a positive, continuous and decreasing function for
Here the infinite sum is
Therefore
So let
Then clearly f(x) is continuous, positive, and decreasing for
Hence Integral Test can be applied for
Now checking for the convergence or divergence of the improper integral
So,
Hence
Therefore by Integral test
Answer: The series
Jeffrey Jordon
Expert2021-12-26Added 2605 answers
Answer is given below (on video)
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