Finding Products of a Range of NumbersDate: 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/ |
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