Task D. Computing Fibonacci Numbers with Loops and Arrays 0, 1, 1, 2, 3, 5, 8, 13

First, a quick intro:

Fibonacci numbers is a sequence of numbers that starts with F(0) = 0 and F(1) = 1, with all the following numbers computed as the sum of two previous ones, F(n) = F(n1) + F(n2):

0 1 1 (=1+0) 2 (=1+1) 3 (=2+1) 5 (=3+2) 8 (=5+3) 13 (=8+5) and so on

To make a C++ program to keep track of the previous numbers so that we can compute the new ones, we can use an array of integers:

// make an array int fib[60]; // first two terms are given fib[0] = 0 fib[1] = 1 // and all the following ones can be computed iteratively as fib[i] = fib[i-1] + fib[i-2] 

The task:

Write a program fibonacci.cpp, which uses an array of ints to compute and print all Fibonacci numbers from F(0) to F(59).

Example:

0 1 1 2 3 5 8 13 ... 

Once your program is complete and works, check carefully the values printed on the screen. Specifically, what is happening when the numbers approach two billions? We expect that at some point the numbers start diverging from what they should be. Describe what you observe and explain why it is happening in a program comment.