Determine whether the series converges or diverges. Give the sum of the convergent series.
The series diverges.
Given a series .
The series is in the standard form for a geometric series with and .
The geometric series converges if and only if .
Since localid="1648966760738" , it follows that the series localid="1648966763917" diverges.
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 if salmon 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?
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