The recursion rule for finding Fibonacci numbers is awkward to use if you want to find,...

The recursion rule for finding Fibonacci numbers is awkward to use if you want to find, for example, the value of 80th number in the sequence, since it requires knowledge of the values of the previous two numbers, which in turn requires knowledge of the values of the previous two numbers, and so on. There is another formula that generates the values of the Fibonacci numbers and does not depend on knowing the value of any other Fibonacci number. It is called Binet’s formula, and it is written explicitly in terms of n, where f_n is the nth Fibonacci number.

a. By letting n = 1, 2, 3, and 4, verify that Binet’s formula generates the first four numbers in the Fibonacci sequence, namely 1, 1, 2, and 3. Use your calculator. Do not use rounded numbers while performing the calculations. Let your calculator keep all possible digits.

b. Use Binet’s formula to find the value of the 40^th Fibonacci number. Use your calculator, and do not use rounded numbers while performing the calculations. Let your calculator keep all possible digits.