Simplifying the Ratio of Factorials: Calculus II?

Question

Can you give me the rules I need to solve problems like these:
25! / 23!

or

(n+2)! / n!

For the first one I came up with:
600

and for the second one I got:
(n+1)(n+2)

Can you tell me if I am wrong or right and why? Thanks. Any info on simplifying the ratio of factorials in calculus II would be great. My book does not go into detail on this subject.

Answer 1

25!/23!= 23!*24*25/23!=24*25=600 i think you got right.
(n+2)!/n!=n!*(n+1)*(n+2)/n!= (n+1)(n+2)
you got all right answers
on the first problem you will know 25 factorial is bigger than 23 !
you can change 25! to 23!*24*25 so you can cancel 23!
you know 25!=(1*2*3....*23)*24*25 but on the parenthesis that is 23! so the 25!is 23!*24*25.
(n+2)! is bigger than n!
you want to distribute (n+2)!
n!(n+1)(n+2) then you can cancel n!
good luck

Answer 2

25!= 1*2*..........25
23! =1*2*.......23 The only factors which don simplify are 24*25=
600.
You were right on both.You must look,as you did,for the factors which are missing for simplification

Answer 3

3n! / (n+a million)! = 3(n)(n-a million)(n-2)...a million / (n+a million)(n)(n-a million)(n-2)... = 3/(n+a million) be conscious that 3n! ? (3n)! regardless of if it somewhat is (3n)! / (n+a million)! there's no thank you to simplify it and once you're doing limits at infinity with this it is going to likely be infinity because of fact (3n)! grows lots, lots swifter.