How do I get the product of all the numbers from a to b?

Question

For example, if a=7 and b=12, then the equation I want will give me the product of 7*8*9*10*11*12.

I like what I see so far, but is there away to do it for negative numbers to? As in: a=-4 and b=-2 so I get (-4)*(-3)*(-2). My calculator wouldn't let me do "-x!".

Answer 1

b!/(a-1)!

So your example would be 12!/6!

Edit: to expand this to cases where a and b are both negative, just compute this as though a and b are both positive and then multiply by (-1)^(b-a+1). In cases where b is positive and a is negative, your answer is always zero (since zero is one of the numbers you're multiplying).

Answer 2

Just do it for positive numbers. Then if there are an odd number of terms, the answer will be negative.

Answer 3

ishaqkhan got it right. You're limiting yourself to integers. If you wanted the numbers, including fractions, etc., you could do a "double integral" on the product xy, each going from a to b.

Answer 4

Assume |a| ≤ |b|
Then P = [|b|!/(|a|-1)!] * (|a|/a)^(|b|-|a|+1) if ab>0
and P=0 if ab≤0

where |x| is the absolute value of x

Answer 5

There is no sort cut fomula you have to multiply

Answer 6

(b!)/(a-1)!

where ! = factorial