Chapter 7: Q. 13 (page 639)
Explain how you could adapt the root test to analyze a seriesin which the terms of the series are all negative.
Short Answer
Hence proved.
Chapter 7: Q. 13 (page 639)
Explain how you could adapt the root test to analyze a seriesin which the terms of the series are all negative.
Hence proved.
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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?
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.
Given a series , in general the divergence test is inconclusive when . For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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