## Manipulation of Factorials

factorial, writtenis– we multiply together all the whole numbers between 1 andinclusive.

Sometimes we have to multiply or divide factorial expressions:.

Ifthen

A common expression isWe often need to divide expressions of the form

The above expression may be all you need, but more terms may be cancelled, though you may not think the resulting expression simpler -assuming

Both expressions are useful in number theory. It should be noted thatis the ratio of two binomial coefficients and can for example be used in the ratio test to find the interval of convergence of a series.

Another common expression isWe often need to divide expressions of the form

The above expression may be all you need, but more terms may be cancelled, though you may not think the resulting expression simpler, again assuming

Both expressions are useful in number theory.