Chapter 7: Q 67. (page 615)
Find the values of x for which the seriesconverges.
Short Answer
The series converges only for.
Chapter 7: Q 67. (page 615)
Find the values of x for which the seriesconverges.
The series converges only for.
All the tools & learning materials you need for study success - in one app.
Get started for freeExamples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) A divergent series in which .
(b) A divergent p-series.
(c) A convergent p-series.
Prove Theorem 7.24 (a). That is, show that if c is a real number and is a convergent series, then .
Find the values of x for which 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?
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
What do you think about this solution?
We value your feedback to improve our textbook solutions.