Homework 3 - CS 630 - Computing Fundementals I

CS 630 - Computing Fundementals I - Spring 2004 Problem 1 - Math Functions

Loyola College > Department of Computer Science > CS 630 > Homework > Problem 1

Objectives

to use C++ Math functions

Introduction

For any integer n > 0, n! is defined as the product 1 * 2 * ... * n. It is sometimes useful to have a closed-form instead; for this purpose an approximation can be used. In 1730 J. Stirling came up with such an approximation, which can be expressed as

Eric Weisstein's World of Mathematics has a page on Stirling's Approximation.

Assignment

Create a program called FactorialApproximator that prompts the user to enter an integer n, calls functions which calculate the lower and upper bounds for n! using Stirling's Approximation, and then displays those bounds in the terminal. The message should look something like this (of course, the actual numbers will depend on the user's input):

1.551104102634359E25 <= 25! <= 1.5511212799620605E25

Hints

Your program will be easier to debug if you use some intermediate values instead of trying to compute the bounds in a single expression. If you are not getting the correct results then you can display the results of your intermediate values and compare them to what you get when you do the calculations by hand.
Pay heed to C++'s precedence and type rules. (Ex: integer vs. double division)

You can use the following function to for the value of pi (Cut and paste this code into your program).

double pi() {

  double series = 0;
  int sign = 1;
  for (int i = 0, j = 1; i < 100; i++, j+=2) {
    series += sign * 1 / (pow(3, i) * j);
    sign *= -1;
  }

  double result = 2 * sqrt(3) * series;
  return result;

}