Project Euler Problem 2
Each new term in the Fibonacci sequence is generated by adding the previous two terms.
Solution
We need the sum of the even Fibonacci numbers not exceeding $4{,}000{,}000$.
The Fibonacci sequence begins:
$$1,2,3,5,8,13,21,34,\dots$$
The even-valued terms are:
$$2,8,34,144,\dots$$
A direct approach is to generate Fibonacci numbers up to $4{,}000{,}000$ and accumulate the even ones.
Python code:
a, b = 1, 2
total = 0
while a <= 4_000_000:
if a % 2 == 0:
total += a
a, b = b, a + b
print(total)
Tracing the computation gives the even Fibonacci terms:
$$2 + 8 + 34 + 144 + 610 + 2584 + 10946 + 46368 + 196418 + 832040 + 3524578$$
Their sum is:
$$4613732$$
Answer: 4613732