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)

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.