Added problems till 60 to ipynb.

ipython/EulerProblem057.ipynb

@@ -0,0 +1,70 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Square root convergents (Euler Problem 57)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "[https://projecteuler.net/problem=57](https://projecteuler.net/problem=57)\n",
+    "\n",
+    "It is possible to show that the square root of two can be expressed as an infinite continued fraction.\n",
+    "\n",
+    "√ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...\n",
+    "\n",
+    "By expanding this for the first four iterations, we get:\n",
+    "\n",
+    "1 + 1/2 = 3/2 = 1.5\n",
+    "\n",
+    "1 + 1/(2 + 1/2) = 7/5 = 1.4\n",
+    "\n",
+    "1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...\n",
+    "\n",
+    "1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...\n",
+    "\n",
+    "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.\n",
+    "\n",
+    "In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
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+   "name": "python3"
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+}