Question

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

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

Answer 1

The correct option is D $1,8,49$

$P\left(n\right)={\sum }_1^{n}r=\frac{n\times (n+1)}{2}$

$P\left(1\right)=1$

$P\left(8\right)=36=$ square of $6$

$P\left(49\right)=1225=$ square of $35$