Continued Fractions Python
Question: I am new to Python and was asked to create a program that would take an input
as a non-negative integer n and then compute an approximation for the value of
e using the first n + 1 terms of the continued fraction:

I have attempted to decipher the question but can't exactly understand
everything it is asking. I am not looking for an exact answer but hopefully an
example to help me on my way.

[This is the exact question](http://i.stack.imgur.com/5zbsz.jpg)  
Below is a code I have done with continued fractions before.

    
    
    import math
    # Get x from user
    x = float(input("Enter x = "))
    
    # Calculate initial variables and print
    a0 = x//1
    r0 = x-a0
    print("a0 =", a0, "\tr0 =", r0)
    
    # Calculate ai and ri for i = 1,2,3 and print results
    
    a1 = 1/r0//1
    r1 = 1/r0 - a1
    print("a1 =", a1, "\tr1 =", r1)
    
    a2 = 1/r1//1
    r2 = 1/r1 - a2
    print("a2 =", a2, "\tr2 =", r2)
    
    a3 = 1/r2//1
    r3 = 1/r2 - a3
    print("a3 =", a3, "\tr3 =", r3)
    


Answer: The value e can be expressed as the limit of the following continued fraction:

> e = 2 + 1 / (1 + 1 / (2 + 2 / (3 + 3 / (4 + 4 / (...)))))

The initial `2 + 1 /` falls outside of the main pattern, but after that it
just continues as shown. Your job is to evaluate this up to `n` deep, at which
point you stop and return the value up to that point.

Make sure you carry out the calculation in floating point.

