{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Quiz 2 : Batch 3"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Find the value of $\\pi$ upto $5$ decimal places by using the following formula.\n",
      "\n",
      "\\begin{equation}\n",
      "    \\pi = \\sum_{n=0}^{\\infty} \\frac{2^{n+1}}{\\binom{2n}{n} (2n + 1)}\n",
      "\\end{equation}\n",
      "\n",
      "Compute the first 30 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": "code",
     "collapsed": false,
     "input": [
      "def compute_pi(N) :\n",
      "    s = 0.0\n",
      "    two_power = 2.0\n",
      "    binom2nn = 1.0\n",
      "    nth_odd = 1.0\n",
      "    for n in range(N) :\n",
      "        s += two_power / binom2nn / nth_odd\n",
      "        two_power *= 2\n",
      "        binom2nn *= float((2*n + 1) * (2*n + 2)) / (n + 1)**2\n",
      "        nth_odd += 2\n",
      "    return s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "val_of_pi = compute_pi(30)\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": {}
  }
 ]
}