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Chapter 7: Q. 23 (page 656)
<img src="https://latex.codecogs.com/svg.image?k!\div&space;(k&space;+&space;2)!" title="https://latex.codecogs.com/svg.image?k!\div (k + 2)!" />
(K+2)(K+1)
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Let andbe two convergent geometric series. Prove that converges. If neither c nor b is 0, could the series be ?
Prove that if converges to L and converges to M , then the series.
In Exercises 48–51 find all values of p so that the series converges.
In Exercises 48–51 find all values of p so that the series converges.
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?
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