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 divergent.
Consider function .
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 divergent.
Hence, by integral test, the series is divergent
For each series in Exercises 44–47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder, .
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that localid="1649224052075" .
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