Is there a formula to find the product of n natural numbers. For example can I determine the value of 19! by the formula.

Asked on by tylak

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The product of n natural numbers can only be found by multiplying the n numbers. There is no formula for that. If you have tables for the factorials of numbers you could find the value of the product of n consecutive natural numbers from 1 to n by looking up for n!

19! = 19*18*17...*1

There is no general formula to find the product of n natural numbers.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

We know that Lt n -> infinity  n!/ {sqrt(2pi*n)(n/e)^n} = 1.

Therefore n! asymptotically behaves like  sqrt((2pi*n)(n/e)^n.

Therefore n! =  sqrt((2pi*n)(n/e)^n approximately. The formula holds better for large n.

Ex 19! = 2.12*10^17.

19! = 2.11*10^17  using formula.

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