Chapter 7: Q. 37 (page 615)
Evaluate the finite sums.
Short Answer
The sum of the seriesis,.
Chapter 7: Q. 37 (page 615)
Evaluate the finite sums.
The sum of the seriesis,.
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Get started for freeExplain 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.
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" .
Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Provide a more general statement of the integral test in which the function f is continuous and eventually positive, and decreasing. Explain why your statement is valid.
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 ?
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