{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using loops to calculate values using numerical methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use a for loop to calculate the value of 1, using a numerical method\n",
    "n=0\n",
    "for i in range(1,5):\n",
    "    n = n + 1/2**i\n",
    "print(f'The approx value of n is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=0\n",
    "for i in range(1,10):\n",
    "    n = n + 1/2**i\n",
    "print(f'The approx value of n is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approx value of n is 1.0\n"
     ]
    }
   ],
   "source": [
    "n=0\n",
    "for i in range(1,10000):\n",
    "    n = n + 1/2**i\n",
    "print(f'The approx value of n is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approx value of pi/4 is 0.8666666666666667\n"
     ]
    }
   ],
   "source": [
    "n = 0\n",
    "for i in range(0,3):\n",
    "    term = (-1)**i / (2*i+1)\n",
    "    n = n + term\n",
    "print(f'The approx value of pi/4 is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7853981633974483\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "print(math.pi/4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approx value of pi/4 is 0.7604599047323508\n"
     ]
    }
   ],
   "source": [
    "n = 0\n",
    "for i in range(0,10):\n",
    "    term = (-1)**i / (2*i+1)\n",
    "    n = n + term\n",
    "print(f'The approx value of pi/4 is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The approx value of pi/4 is 0.7853731633975086\n"
     ]
    }
   ],
   "source": [
    "n = 0\n",
    "for i in range(0,10000):\n",
    "    term = (-1)**i / (2*i+1)\n",
    "    n = n + term\n",
    "print(f'The approx value of pi/4 is {n}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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