Question

If(n+2)! = 2550n! Find the value of n

Answer 1

Step-by-step explanation:

We know

n!= n(n-1)(n-2)(n-3)(n-4)...

(n+2)!=(n+2)(n+1)n!

Let take Example to understand why (n+2)!=(n+2)(n+1)n!

Let take n=3

(3+2)!=5!=5×4×3! [3!=1×2×3]

So,

(n+2)!=2550n!

(n+2)(n+1)n!=2550n!

n! cancelled

(n+1)(n+2)=2550

n²+2n+n+2=2550

n²+3n+2-2550

n²+3n-2548

n²-52n+49n-2548

n(n-52)+49(n-52)

(n+49)(n-52)

n=-49

n=52

Hence n=52