CS 630 - Computing Fundamentals I

CS 630 - Computing Fundamentals I - Fall 2005 Homework 4

Loyola College > Department of Computer Science > CS 630 > Homework > Homework 4

Due

Monday, October 10th at the beginning of class

Problems

Exercise (pp. 152-153)
3.2
3.3
3.7

(4) Using Math.Random write a statement that will produce a number between the following endpoints:
(a) 0 to 10
(b) 1 to 10
(c) -10 to 15

Programming Project
3.3 (pg. 153)

Factorial Approximation (myCodeMate DL0099)

Objectives

to use functions from the Java Math class

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

This is the square root of 2 pi.

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

Assignment

Create a program called FactorialApprox that prompts the user to enter an integer n, calculates the lower and upper bounds for n! using Stirling's Approximation, and then outputs those bounds. 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 should give exact answers for 1 through 7. At some point beyond 100 it will likely overflow; do not worry about this.
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 Java's precedence and type rules. (Ex: integer vs. double division)
You can use the expression Math.PI for the value of pi.