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  4. For every natural number n, n(n2 - 1) is divisible by

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

Principle of Mathematical Induction

Solution:

$n(n^2 -1) = (n -1)(n)(n +1)$ It is product of three consecutive natural numbers, so according to Langrange’s theorem it is divisible by $3!$ i.e., $6$