Chapter 7: Q. 8 (page 624)
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
Short Answer
By the integral test, the series is divergent.
Chapter 7: Q. 8 (page 624)
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
By the integral test, the series is divergent.
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Get started for freeExpress each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
35.
Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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 ?
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.
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