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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quiz 2 : Batch 4"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find the value of $\\pi$ upto $5$ decimal places by using the following formula.\n",
      "\n",
      "\\begin{equation}\n",
      "    \\frac{1}{\\pi} = \\frac{2\\sqrt{2}}{9801} \\sum_{k=0}^{\\infty} \\frac{(4k)! (1103 + 26390k)}{(k!)^4 396^{4k}}\n",
      "\\end{equation}\n",
      "\n",
      "Compute the first $20$ terms of this series to compute $\\pi$ and print the answer upto 5 decimal places."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "####Grading scheme.\n",
      "* Total points : 10 marks\n",
      "* -5 if any kind of loop (while or for) is not used to compute the sum\n",
      "* -2 if the logic is correct but the code is not running due to syntax error\n",
      "* -1 is not upto the specification of 5 decimal spaces."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Sample solution"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "def compute_inv_pi(N) :\n",
      "    Const = 2.0 * math.sqrt(2) / 9801\n",
      "    s = 0.0\n",
      "    fact4k = 1.0\n",
      "    factk_to_4 = 1.0\n",
      "    inv_power_396_4k = 1.0 \n",
      "    linterm = 1103.0 # 1103 + 26390k\n",
      "    for k in range(N) :\n",
      "        s += (fact4k * linterm * inv_power_396_4k) / factk_to_4\n",
      "        fact4k *= (4*k + 1) * (4*k + 2) * (4*k + 3) * (4*k + 4)\n",
      "        factk_to_4 *= (k + 1)**4\n",
      "        inv_power_396_4k /= 396**4\n",
      "        linterm += 26390\n",
      "    inv_pi = Const * s\n",
      "    return inv_pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "val_of_pi = 1.0 / compute_inv_pi(20)\n",
      "print \"The value of pi is %7.5f.\" % val_of_pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of pi is 3.14159.\n"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}