Fibonacci and Lucas

Math 242 practice problems

Name: _________________

Learning Goals: Formulate precise mathematical conjectures supported by computational evidence. Explore generalizations of known mathematical ideas.

Your task: Towards the end of class today we introduced the Lucas numbers. Use your code for computing the Fibonacci and Lucas numbers to complete the two problems from the text reprinted below.

Due: Monday, March 7, at 5:00pm. Upload your solution as a Mathematica notebook to the Fibonacci and Lucas assignment (Moodle link).

Grading: If you complete each problem below, you will earn a Satisfactory grade.

Need help? Review the notes from class, which are posed on the course web site. If you still need help, email Prof. Wright.

Practice 2.41: Verify that the Fibonacci and Lucas numbers satisfy (Subscript[L, n])=(Subscript[F, n-1])+(Subscript[F, n+1]). Show that this identity holds for at least 100 values of n.

Exercise 2.42: What happens if you multiply the Lucas numbers by the corresponding Fibonacci numbers? Investigate the product (Subscript[F, n])(Subscript[L, n]) for various integers n. Conjecture an identity whose left side is (Subscript[F, n])(Subscript[L, n]).