Gujarat BoardEnglish MediumSTD 6MATHSWhole Numbers1 Mark
MCQ
$n^2 + n + 1$ is a or an ______ number for all $\text{n}\in\text{N}$
A
Even
✓
Odd
C
Prime
D
None of these
✓
Answer
Correct option: 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.
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