Question

If (n + 2)! = 60*(n - 1)!, find n​

Answer 1

Answer:

GOOD QUESTION

Step-by-step explanation:

ANSWER IS 58

Answer 2

Answer:

We have,

(n+2)!=60(n−1)

As we know n!=(n−1) n!

Therefore,

(n+2)(n+1)n×(n−1)!=60(n−1)!

(n+2)(n+1)n=60

(n2+2n+n+2)n=60

(n 3 +3n 2 +2n−60)=0

⇒n3+3n2+2n−60=0

Factoring the left hand side, this equation resolves to

(n−3)(n  2 +6n+20)=0(n−3)(n2+6n+20)=0

Since it can be shown that(n2+6n+20)=0 has (n 2+6n+20)=0 no real solution,  

n−3=0

n=3

Hence, the value of n is 3.