bY PMI prove n(n+1)(2n+1) is divisible by 6

Let the given statement be P(*n*) i.e.,

For *n* = 1, we have

Let P(*k*) be true for some positive integer *k*, i.e.

We shall now prove that P(*k* + 1) is true.

∴ P(*k*) is true ⇒ P(*k *+ 1) is true.

Hence, by the principle of mathematical induction, statement P(*n*) is true for all natural numbers *n*.

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