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Chapter 7: Q. 88 (page 605)
Prove Theorem 7.14. That is, show that if is a sequence that converges to L, then every subsequence of also converges to L
Proved that every subsequence of the sequence converges to the same limit L
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Leila finds that there are more factors affecting the number of salmon that return to Redfish Lake than the dams: There are good years and bad years. These happen at random, but they are more or less cyclical, so she models the number of fish returning each year as , where h is the number of fish whose spawn she releases from the hatchery annually.
(a) Show that the sustained number of fish returning in even-numbered years approach approximately
(Hint: Make a new recurrence by using two steps of the one given.)
(b) Show that the sustained number of fish returning in odd-numbered years approaches approximately
(c) How should Leila choose h, the number of hatchery fish to breed in order to hold the minimum number of fish returning in each run near some constant P?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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.
Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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