**Problem 2**

*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.*

**Solution**

namespace ProjectEulerCSharp_002

{

//By considering the terms in the Fibonacci sequence

//whose values do not exceed four million, find the

//sum of the even valued terms.

class Program

{

static void Main(string[] args)

{

int answer = 0;

//typically when calculating fibonacci series

//it’s performed two elements at a time

//this is not a requirement

int fib0 = 1;

int fib1 = 1;

int fib2 = 2;

while (fib2 < 4000000)

{

//we know the fib2

//is always even

//and represents ALL

//evens in the series

//see the ‘proof’ below

answer += fib2;

//odd + even = odd

fib0 = fib1 + fib2;

//odd + even = odd

fib1 = fib0 + fib2;

//odd + odd = even

fib2 = fib0 + fib1;

}

System.Console.WriteLine(answer);

}

}

}

**Discussion**

As I mentioned in the F# solution, an obvious optimization is to sum as you go. I’ve also taken it a step further and removed the check for evenness because every third Fibonacci is even. I layout a rough proof in my comments above.

If you have questions, leave a comment or please find me on Twitter (@azzlsoft) or email (rich@azzlsoft.com).