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

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 product of three consecutive natural

numbers, so according to Langrange's theorem

it is divisible by 3 ! i.e., 6.

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