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   "source": [
    "# Even Fibonacci Numbers\n",
    "> Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first terms will be:\n",
    "> $$1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \\ldots$$\n",
    "> By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.\n",
    "\n",
    "There's a lot to learn about the [Fibonacci numbers](https://en.wikipedia.org/wiki/Fibonacci_sequence), and this will not be the last time we see them in a Project Euler problem, but for now this problem keeps it relatively simple.\n",
    "\n",
    "Since this is a SageMath notebook, we'll use its functionality so we can keep our code simple like the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "57b68465",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4613732"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(n for n in fibonacci_xrange(1, 4000000) if n % 2 == 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eef788da",
   "metadata": {},
   "source": [
    "Even without SageMath, it's easy to implement our own generator of the sequence up to $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "24a7c257",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fib(n):\n",
    "    a = 0\n",
    "    b = 1\n",
    "    while a <= n:\n",
    "        yield a\n",
    "        a, b = b, a + b"
   ]
  }
 ],
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