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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quiz 2 : Batch 1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find the value of $\\pi$ by computing the first $20$ terms of the series\n",
      "\n",
      "\\begin{equation}\n",
      "\\sqrt{12} \\sum_{k=0}^{\\infty} \\left(- \\frac{1}{3}\\right)^k \\frac{1}{2k+1}\n",
      "\\end{equation}\n",
      "\n",
      "and print the answer to the first 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",
      "\n",
      "def compute_pi(N) :\n",
      "    Const = math.sqrt(12)\n",
      "    power_of_third = 1.0\n",
      "    ith_odd = 1.0\n",
      "    sum_for_pi = 0\n",
      "    for i in range(N+1) :\n",
      "        sum_for_pi += power_of_third / ith_odd\n",
      "        power_of_third *= - 1.0 / 3.0\n",
      "        ith_odd += 2\n",
      "    val_of_pi = Const * sum_for_pi\n",
      "    return val_of_pi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"The value of pi is %7.5f.\" % compute_pi(20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The value of pi is 3.14159.\n"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}