One of the more interesting search techniques uses the Fibonacci sequence. This search method can be employed even if the function is not continuous. The method uses the Fibonacci numbers to place test points for the search. These Fibonacci numbers are defined as follows: F₀=F₁=1 and F_n=F_n–1+F_n–2, for n = 2, 3, 4,......, yielding the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 510, 887, 1397, and so forth.

a. Find the ratio between successive Fibonacci numbers using the preceding sequences. Then find the numerical limit as n gets large. How is this limiting ratio related to the Golden Section Search Method?

b. Research and make a short presentation on the Fibonacci Search Method. Present your results to the class.