Compute Fibonacci Number

source: Tino Duong, 2003

Description:

The Fibonacci sequence is a special number progression where the Nth number can be defined by the two previous numbers in the sequence. Therefore, if we denote the n^th term by f_n, then by the definition f_n = f_n-2 + f_n-1. The 0^th term is accepted as 1. By our rule one can produce all the terms in the sequence. . The first few Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, ...

Your job is to write a program that will compute the Nth number in the Fibonacci sequence.

Requirements:

The program must prompt the user for the Nth number in the sequence they wish to find.
The program must find the Nth number in the sequence using an iterative approach
The program must find the Nth number in the sequence using a recursive approach

The output should look similar to this:

    This program will enter the Nth number of the Fibonacci sequence
    Enter the Nth number now
    9
    Done iteratively, the value is : 34
    Done recursively, the value is : 34

Written Section:

When the Nth number gets large, you'll find that the recursive method is much slower than the iterative method. Explain why this happens.

Additional Requirements:

Write the function so it writes the entire sequence to a file called "fibSequence.txt"

Concepts:

Recursion
Functions
Algorithms

Additional Concepts:

File Input/Output