Concept explainers
a.
To find: the Fibonacci sequence.
a.
Answer to Problem 47E
Fibonacci sequence is:
Explanation of Solution
Given information: Suppose that rabbits live forever and that every month each pair.
produces a new pair which becomes productive at age 2 months. If we start with one newborn pair.
Calculation:
Let
In the nth month, each pair older than 2 months (
Produces a new pair to add to the
So, the number of rabbit pairs in the nth month is:
So, Fibonacci sequence is:
b.
To show: that
b.
Answer to Problem 47E
The limit of {
Explanation of Solution
Given information: Let
Fibonacci sequence is:
Calculation:
Hence proved.
If exist
So,
Since M must be positive, the conclusion is
So, the limit of {
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning