Question

Find n, if:
(n + 1)! = 42 (n - 1)!

Answer 1

(n+1)=42(n-1)
by multipling
n+1=42n-42
-42n+n=-42-1
-41n=-43
n=-43/-41
n=1.0487

Answer 2

Answer:

n =  6 ,-7

Step-by-step explanation:

In this question

We need to find the value of n if

(n + 1)! = 42 (n - 1)!

According to the question,

n(n + 1)(n -1)! = 42 (n - 1)!

Cancelling (n - 1)! from both the sides we get,

n(n + 1) = 42

$n^{2}\ +\ n\ =\ 42$

$n^{2}\ +\ n\ -\ 42\ =\ 0$

$n^{2}\ +\ 7n\ -\ 6n\ -\ 42\ =\ 0$

n(n + 7) - 6(n + 7) = 0

(n - 6)(n + 7) = 0

n = 6 ; n= -7

Hence the value of n is 6 and -7