Associated Topics || Dr. Math Home || Search Dr. Math

### Finding Products of a Range of Numbers

```
Date: 03/28/2002 at 17:55:21
From: M
Subject: Formula for finding products of a range of numbers

What method or formula is there to solve for the product of a range
of numbers? For example, how can I figure out the product of the
numbers from 1 to 100? I know the method for finding the sum of a
range of numbers, but does it have anything to do with the product?
```

```
Date: 03/29/2002 at 11:26:18
From: Doctor Ian
Subject: Re: Formula for finding products of a range of numbers

Hi M,

The product

1 * 2 * 3 * 4 * ... * N

has a special name: N factorial, which is abbreviated N! .  So

1! = 1
2! = 2 * 1
3! = 3 * 2 * 1

and so on.  Note that

N! = N * (N-1)!

which is another way to define 'factorial'.

For large values of N, this grows very quickly, and is difficult to
calculate. However, there are approximations, e.g.,

Calculating N Factorial
http://mathforum.org/dr.math/problems/charles.10.26.99.html

What if the range of numbers doesn't start with 1?

101 * 102 * ... * 199 * 200

1 * 2 * 3 * ... * 99 * 100 * 101 * ... * 200
= --------------------------------------------
1 * 2 * 3 * ... * 99 * 100

200!
= ----
100!

More generally, if for the range from A to B, the formula would be

B!
-------
(B - A)!

There's no real connection between the sum of the numbers from A to B,
and the product of those numbers.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search