Question

$n^2+n+1$ is a or an ______ number for all $n\in N$

• A. even
• B. odd
• C. prime
• D. none of these

Answer 1

The correct option is B odd

Consider $n^2+n=n(n+1)$
We know that if $n$ is a number , then $n+1$ will be its consecutive number
And product of a number and its consecutive number is always even. For example, $2\times 3=6;9\times 10=90$
And as $n^2+n$ is an even number. Then
$n^2+n+1$ will be the next consecutive number of the even number , which is an odd number.
Hence, $n^2+n+1$ will always be an odd number for all natural numbers.