Q59 / 170 · Manipal (MET) 2019 · Mathematics
If $n$ be any integer, then $n(n+1)(2 n+1)$ is:
- Aodd number
- Correct answerBintegral multiple of 6
- Cperfect square
- Ddoes not necessarily have any of the foregoing proof
Solution
Given that $n$ be any integer, then $n(n+1)(2 n+1)$ always an integral multiple of even numbers (i.e. $6,30,84, \ldots$ ) when
$\begin{aligned}
& n=1, n(n+1)(2 n+1)=1(2)(3)=6 \\
& n=2, n(n+1)(2 n+1)=2(3)(5)=30
\end{aligned}$
and so on.
Hence, the correct answer is option: 'B'.