02 Kata [java] - sum of even fibonacci numbers

Here is the first tentative using brute force.

public long sum() {
 long sum = 0;

 for (int i = 1; i < 1000000; i++) {
  long fibNum = fib(i);

  if (fibNum > 4000000) {
   break;
  }

  if (isEven(fibNum)) {
   sum += fibNum;
  }
 }
 
 return sum;
}

private boolean isEven(long n) {
 return (n % 2) == 0;
}

private long fib(long n) {
 return (n < 2) ? n : fib(n - 1) + fib(n - 2);
}

And here is the second tentative using a little big of math magic.

public long sum(double limit) {
 long n = Math.round(((Math.log(limit * Math.sqrt(5))) * 2) + 1.618);
 long sum = 0;

 for (long i = 6; i < n; i++) {
  long fib = (4 * fib(i - 3)) + fib(i - 6);

  if (fib % 2 == 0)
   sum += fib;
 }

 return sum + 2;
}

private long fib(long n) {
 return (n < 2) ? n : fib(n - 1) + fib(n - 2);
}