problem2.py

# Each new term in the Fibonacci sequence is generated by
# adding the previous two terms. By starting with 1 and 2, 
# the first 10 terms will be:
#
# 1,  2,  3,  5,  8, 13, 21, 34,  55, 89, ...
# 
# Find the sum of all the even-valued terms in the sequence
# which do not exceed four million.
#
# Answer: 461372

# A recursive function makes the most sense dealing with 
# Fibonacci numbers since the value of any number depends on
# every previous number

# User only needs to define the ceiling (largest number above
# which to stop)
def sumEvenFib(ceiling, total = 0, prev = 1, this = 2):
    next = prev + this
    if this <= ceiling:
        # if this is even, add it to the total and pass along
        if not (this % 2):
            return sumEvenFib(ceiling, total + this, this, next)
        # otherwise just pass along the current total
        else:
            return sumEvenFib(ceiling, total, this, next)
    else:
        return total

if __name__ == "__main__":
   print sumEvenFib(4000000)