State which of the following statements is true. For every integer n, n(n+2) is divisible by _________.

Question

Q. State which of the following statements is true. For every integer

n, n (n + 1) (n + 2)

is divisible by

Answer 1

Putting n=1
n(n+1)(n+2)=1

××2

××3=6
Putting n=2
n(n+1)(n+2)=2

××3

××4=24
Hence for every integer n the expression
n(n+1)(n+2) is divisible by 6.

The correct option is B 6Putting n=1n(n+1)(n+2)=1××2××3=6Putting n=2n(n+1)(n+2)=2××3××4=24Hence for every integer n the expressionn(n+1)(n+2) is divisible by 6.