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Chapter 7: Q. 60 (page 592)
In Exercises 59–62 use the derivative test in Theorem 7.6 to analyze the monotonicity of the given sequence.
The given sequence is strictly increasing.
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Given that and , find the value of.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
Find the values of x for which the series converges.
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.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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