Question

If k is a positive integer, then $k(k+1)(k+3)$ is

• A. even only when k is even
• B. even only when k is odd
• C. Always odd
• D. Always even

Answer 1

The correct option is D Always even

Suppose $k$ is even

Then $k(k+1)(k+3)$ is even as $k$ will be divisible by $2$

Now if $k$ is odd.

Then $(k+1)$ and $(k+3)$ are even

$\Rightarrow k(k+1)(k+3)$ is also even.

So $k(k+1)(k+3)$ is always even.

So option $D$ is correct.