Chapter 7: Q. 31 (page 615)
Provide the first five terms of the sequence of partial sums for the given series.
Short Answer
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Chapter 7: Q. 31 (page 615)
Provide the first five terms of the sequence of partial sums for the given series.
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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.
Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish returning each year as , where h is the number of fish whose spawn she releases from the hatchery annually.
(a) Show that the sustained number of fish returning in even-numbered years approach approximately
(Hint: Make a new recurrence by using two steps of the one given.)
(b) Show that the sustained number of fish returning in odd-numbered years approaches approximately
(c) How should Leila choose h, the number of hatchery fish to breed in order to hold the minimum number of fish returning in each run near some constant P?
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.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
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.
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