Question

Express the given product or quotient as a factorial expression. Assume that n > r > 0.

1. (n+1)n!

2. (n+8)!/n+8

3. 100 x 99 x 98

4. (n-1)(n-2)(n-3)

Answer 1

1.) (n+1)n! = (n+1)!


2.) (n+8)!/n+8 = (n+8)!/(n+8)
= (n+8)*(n+8-1)! / (n+8) = ((n+8)*(n+7)!) / (n+8)
Cancel out the (n+8)
= (n +7)!


3.) 100 x 99 x 98 = (100 x 99 x 98 x 97!) / (97!) = (100!) / (97!).

4. (n-1)(n-2)(n-3) = ((n-1)(n-2)(n-3)(n-4)!) /(n-4)!
= (n-1)! / (n-4)!.

Cheers. That's it.