SOLUTION: QUESTIONS: simplify the ratio of the following factorials (n+2)! / n!

Algebra ->  Sequences-and-series -> SOLUTION: QUESTIONS: simplify the ratio of the following factorials (n+2)! / n!      Log On


   

Question 924384: QUESTIONS: simplify the ratio of the following factorials
(n+2)! / n!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
(n+2)! / n! is equal to:

(n+2) * (n+1) * n! / n! which is equal to n+2 * n+1

an example will help clarify the concept.

assume n = 6

n+2 must be equal to 8

(n+2)! = 8*7*6*5*4*3*2*1

n! = 6*5*4*3*2*1

since 6*5*4*3*2*1 = 6!, you get:

8! = 8*7*6!

8! / 6! = 8*7*6! / 6! = 8*7 = 56