Approximate exponent using continuous fractions

approx.py

def approximate_exponent(end):
    denominator = float(end) + 1
    for i in xrange(end, 0, -1):
        denominator = i + i/denominator

    return 2+1/denominator


print approximate_exponent(2) #  2.72727272727
print approximate_exponent(3) #  2.71698113208