Chapter 7: Q. 24 (page 631)
In Exercises use one of the comparison tests to determine whether the series converges or diverges. Explain how the given series satisfies the hypotheses of the test you use.
.
Short Answer
The seriesis convergent.
Chapter 7: Q. 24 (page 631)
In Exercises use one of the comparison tests to determine whether the series converges or diverges. Explain how the given series satisfies the hypotheses of the test you use.
.
The seriesis convergent.
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Get started for freeLeila 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?
For each series in Exercises 44–47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder, .
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that localid="1649224052075" .
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.
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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