Chapter 7: Q. 4 (page 591)
What is a term of a sequence?
Each number in the sequence is called a term.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Determine whether the series converges or diverges. Give the sum of the convergent series.
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.
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
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?
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
What do you think about this solution?
We value your feedback to improve our textbook solutions.
