Question

If $1+2+3+\cdots +k=N^2$ and N is less than 100, then the value of k can be (where N $\in$ Natural numbers)

• A. 8
• B. 1 and 49
• C. 8 and 36
• D. both (a) and (b)

Answer 1

The correct option is D both (a) and (b)

Go through options
$1+2+3+\cdots +k=N^2$ (a perfect square)
$\frac{k(k+1)}{2}=N^2$
$\frac{1\times 2}{2}=(1{)}^2\to$ a perfect square number,
$\frac{8\times 9}{2}=4\times 9=(2\times 3{)}^2\to$ a perfect square number.
and $\frac{49\times 50}{2}=49\times 25=(7\times 5{)}^2\to$ a perfect square number.