Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
Ans: The series is convergent.
Consider function .
The first derivative of the function is:
The derivative is negative for all . Therefore the function is decreasing.
The function is continuous, decreasing, with positive terms. Therefore, all the conditions of the integral test are fulfilled. So, the integral test is applicable.
The integral converges. Therefore, the series is convergent.
Hence, by integral test, the series is convergent.
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