Chapter 7: Q. 31 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
Short Answer
The first five terms are.
Chapter 7: Q. 31 (page 592)
In Exercises 31–36 provide the first five terms of the given sequence. Unless specified, assume that the first term has index 1.
The first five terms are.
All the tools & learning materials you need for study success - in one app.
Get started for freeUse 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.
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?
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that , What can the integral tells us about the series ?
Determine whether the series converges or diverges. Give the sum of the convergent series.
True/False:
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) True or False: If , then converges.
(b) True or False: If converges, then .
(c) True or False: The improper integral converges if and only if the series converges.
(d) True or False: The harmonic series converges.
(e) True or False: If , the series converges.
(f) True or False: If as , then converges.
(g) True or False: If converges, then as .
(h) True or False: If and is the sequence of partial sums for the series, then the sequence of remainders converges to .
What do you think about this solution?
We value your feedback to improve our textbook solutions.