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  4. If P(n) = n3 + (n + 1)3 + (n+ 2)3 where n ∈ N then P(n) is divisible by

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Q. If $P(n) = n^{3} + (n + 1)^{3} + (n+ 2)^{3}$ where n $\in$ N then P(n) is divisible by

Principle of Mathematical Induction

Solution:

Let $n = 1,$
$\therefore P (1)= 1+8 + 27 = 36$
$\therefore P(1) = 36$ is divisible by $9$