Euler.2.ipynb

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    "#Project Euler\n",
    "### Problem 2\n",
    "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:\n",
    "\n",
    "1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...\n",
    "\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",
    "___"
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    "limit = 4*(10**6)"
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    "Note that: even + even = even, uneven + even = uneven, uneven + uneven = even. \n",
    "\n",
    "Hence Fibonacci shows:\n",
    "uneven, even, uneven, uneven, even, uneven, uneven, even, ...\n",
    "\n",
    "We thus need to sum the values on places: $2+3*x$.\n",
    "\n",
    "Explicit formula for Fibonacci on $n^{th}$ place is:\n",
    "\n",
    "$$f_n = \\frac{(1 + \\sqrt{5})^n - (1 - \\sqrt{5})^n}{2^n \\sqrt{5}}$$"
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