Chapter 7: Q. 36 (page 615)
Provide the first five terms of the sequence of partial sums for the given series.
.
Short Answer
The first five terms of the partial sums for the seriesis,.
Chapter 7: Q. 36 (page 615)
Provide the first five terms of the sequence of partial sums for the given series.
.
The first five terms of the partial sums for the seriesis,.
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Get started for freeGiven 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.
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?
Determine whether the series converges or diverges. Give the sum of the convergent series.
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.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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