Summation that gives perfect squares

Question

For $n=1,2,3,4$ upto $50$. How many $s(n)$ will be perfect squares?

The answer given is $3(n=1,8,49)$. What will be the approach for such questions?

Answer 1

$$s(n)=\frac{n.(n+1)}{2}$$ now you need to make sure this is a perfect square , now note all factors of $n$ will not be a factor of $n+1$ except for $1$ thus you need the odd term to be a perfect square and even term to be $2.a$ where $a$ is a perfect square. now cases are significantly reduced , consider all odd squares till $50$ and check the cases