For every natural number n, n ( n 2 − 1 ) is divisible by Options: A . &nbsp 4 B . &nbsp 6 C . &nbsp 10 D . &nbsp None of these

For every natural number n, n(n2−1) is divisible by

Discussion Forum : Principle Of Mathematical Induction

Question -

For every natural number n, n $(n^{2} - 1)$ is divisible by

Options:

A . 4

B . 6

C . 10

D . None of these

Answer: Option B
:
B

$n (n^{2} - 1) = (n - 1) (n) (n + 1)$

It is the product of three consecutive natural numbers. For any three consecutive natural numbers, one of them is divisible by 3 and at least one is divisible by 2. Hence, the product is always divisible by 6.

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