Chapter 7: Q. 31 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
Short Answer
The first five terms are.
Chapter 7: Q. 31 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
The first five terms are.
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Improper Integrals: Determine whether the following improper integrals converge or diverge.
Leila, 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?
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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