Fibonacci and Lucas II

Math 242 practice problems

Name: _________________

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

Your task: Use your code for computing the Fibonacci and Lucas numbers to complete the two problems from the text reprinted below.

Due: Wednesday, March 9, 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.

Exercise 2.55: Find an identity of the form (Subscript[F, 3n])=(Subscript[F, n])(a (Subscript[L, n]^2)+b (Subscript[L, n]^1)+c ). State your conjecture, supported by computational evidence.

Exercise 2.56: Find an identity of the form (Subscript[F, 4n])=(Subscript[F, n])(a (Subscript[L, n]^3)+b (Subscript[L, n]^2)+c  (Subscript[L, n])). State your conjecture, supported by computational evidence.