sicp exercise 13

sicp's exercise no. 13
what do i need to solve this? can i do it with mathematical induction?
i saw that last semester, but didn't quite get it. i'll review it if it's necessary.

>>12

lrn2 optimize effort.

1) Download/Open Maple or some other math program that does symbolic manipulation.

2) Verify that (φ^0 - ψ^0) / √5 = 0, (φ^1 - ψ^1) / √5 = 1, and (φ^n - ψ^n) / √5 + (φ^(n+1) - ψ^(n+1)) / √5.  (http://i39.tinypic.com/350nixi.jpg)

3) Since Fib(n) = (φ^n - ψ^n) / √5 and φ^n / √5 differ by a quantity less than .5, Fib(n) is the nearest integer.