Question

For any $+$ve integer $n,n^3+2n$ is always divisible by

• A. $3$
• B. $7$
• C. $5$
• D. $6$

Answer 1

Answer: (A)

$3$

Let $P\left(n\right)=n^3+2n$

Now $P\left(1\right)=1^3+2\left(1\right)=3$, divisible by $3$

$P\left(2\right)=2^3+2\left(4\right)=12$, divisible by $3$ and $6$

$P\left(3\right)=3^3+2\left(3\right)=33$, divisible by $3$

Hence $n^3+2n$ is divisible by $3$