Chapter 7: Q. 9 (page 591)
Give a recursive definition for the sequence of positive integers. (Hint: Let .)
Short Answer
The recursive definition for the sequence iswhere.
Chapter 7: Q. 9 (page 591)
Give a recursive definition for the sequence of positive integers. (Hint: Let .)
The recursive definition for the sequence iswhere.
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Get started for freeAn Improper Integral and Infinite Series: Sketch the function for x ≥ 1 together with the graph of the terms of the series Argue that for every term of the sequence of partial sums for this series,. What does this result tell you about the convergence of the series?
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?
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.
If a positive finite number, what may we conclude about the two series?
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