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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

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