def prob2(limit=4000000):
    """
    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, ...

    By considering the terms in the Fibonacci sequence whose values do not
    exceed four million, find the sum of the even-valued terms.
    """
    a = 0
    n1 = 1
    n2 = 2
    while True:
        t = n1 + n2
        n1 = n2
        n2 = t
        if n2 > limit:
            break
        if n2 % 2 == 0:
            a += n2
    return a + 2