Chapter 7: Q 69. (page 615)
Find the values of x for which the series converges.
Short Answer
The series converges for all real numbers except for .
Chapter 7: Q 69. (page 615)
Find the values of x for which the series converges.
The series converges for all real numbers except for .
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Get started for freeLeila, in her capacity as a population biologist in Idaho, is trying to figure out how many salmon a local hatchery should release annually in order to revitalize the fishery. She knows that ifsalmon spawn in Redfish Lake in a given year, then only fish will return to the lake from the offspring of that run, because of all the dams on the rivers between the sea and the lake. Thus, if she adds the spawn from h fish, from a hatchery, then the number of fish that return from that run k will be .
(a) Show that the sustained number of fish returning approaches as k→∞.
(b) Evaluate .
(c) How should Leila choose h, the number of hatchery fish to raise in order to hold the number of fish returning in each run at some constant P?
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.
37.
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.
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.
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.
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