Simplify the ratio of factorials.
(n+2)!/(n-1)!
isn't (n+2)!=(n+2)(N+1)(n)(n-1)! ?
To simplify the ratio of factorials (n+2)!/(n-1)!, we can cancel out the common factors between the numerator and the denominator.
The numerator (n+2)! can be expanded as (n+2)(n+1)n!.
The denominator (n-1)! can be expanded as (n-1)(n-2)!
Now, we can cancel out the common factors:
(n+2)!/(n-1)! = [(n+2)(n+1)n!]/[(n-1)(n-2)!]
Canceling out the common factors:
= (n+2)(n+1)
So, the simplified ratio of factorials (n+2)!/(n-1)! is (n+2)(n+1).
To simplify the ratio of factorials (n+2)!/(n-1)!, we can first expand the factorials:
(n+2)! = (n+2)(n+1)n(n-1)!
(n-1)! = (n-1)(n-2)...
Now we can cancel out common terms between the numerator and denominator:
(n+2)!/(n-1)! = [(n+2)(n+1)n(n-1)!] / [(n-1)(n-2)...]
Notice that (n-1)! appears in both the numerator and denominator. We can cancel these terms out:
(n+2)!/(n-1)! = [(n+2)(n+1)n] / [(n-2)...]
The final simplified expression is:
(n+2)(n+1)n / (n-2)...