057-square-root-convergents.ipynb

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    "# Square root convergents\n",
    "## Problem 57 \n",
    "\n",
    "<div class=\"problem_content\" role=\"problem\">\n",
    "<p>It is possible to show that the square root of two can be expressed as an infinite continued fraction.</p>\n",
    "<p style=\"text-align:center;\">&#8730; 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...</p>\n",
    "<p>By expanding this for the first four iterations, we get:</p>\n",
    "<p>1 + 1/2 = 3/2 = 1.5<br/>\n",
    "1 + 1/(2 + 1/2) = 7/5 = 1.4<br/>\n",
    "1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...<br/>\n",
    "1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...<br/></p>\n",
    "<p>The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator.</p>\n",
    "<p>In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?</p>\n",
    "</div>"
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   "source": [
    "def solve():\n",
    "    # Your code here\n",
    "    \n"
   ]
  },
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   "source": [
    "## Solution"
   ]
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   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "solve()"
   ]
  }
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