Chapter 7: Q. 4 (page 652)
Find an example of a divergent series of the form
(a) that satisfies conditions (i) and (iii), but not condition (ii);
(b) that satisfies conditions (i) and (ii), but not condition (iii).
Short Answer
(i)
Chapter 7: Q. 4 (page 652)
Find an example of a divergent series of the form
(a) that satisfies conditions (i) and (iii), but not condition (ii);
(b) that satisfies conditions (i) and (ii), but not condition (iii).
(i)
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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.
In Exercises 48–51 find all values of p so that the series converges.
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?
Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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