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  4. If 'n ' is a positive integer, then n3 + 2n is divisible by

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Q. If $'n '$ is a positive integer, then $n^3 + 2n$ is divisible by

KCETKCET 2009Permutations and Combinations

Solution:

Let $P(n)=n^{3}+2 n$
$\Rightarrow P(1)=1+2=3$
$\Rightarrow P(2)=8+4=12$
$\Rightarrow P(3)=27+6=33$
Here, we see that all these numbers are divisible by $3 .$