Chapter 7: Q. 55 (page 592)
In Exercises 55– 58 use the ratio test in Theorem 7.6 to analyze the monotonicity of the given sequence.
Short Answer
The given sequence is eventually decreasing for
Chapter 7: Q. 55 (page 592)
In Exercises 55– 58 use the ratio test in Theorem 7.6 to analyze the monotonicity of the given sequence.
The given sequence is eventually decreasing for
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Get started for freeFor 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" .
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that role="math" localid="1649081384626" . What can the divergence test tell us about the series ?
Explain why, if n is an integer greater than 1, the series diverges.
For a convergent series satisfying the conditions of the integral test, why is every remainder positive? How can be used along with the term from the sequence of partial sums to understand the quality of the approximation ?
Determine whether the series converges or diverges. Give the sum of the convergent series.
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