Question

If $P\left(n\right)=1+2+3+\dots +n$ is a perfect square $N^2$ and $N$ is less than $100$, then possible values of $n$ are

• A. only $1$
• B. $1$ & $8$
• C. only $8$
• D. $1,8,49$

Answer 1

Answer: (D)

$1,8,49$

The value of $n$ is to be calculated.
By trying the options, we get that $1,8,49$ satisfy the given criteria.
$P\left(n\right)=\frac{n(n+1)}{2}$