Question

Think about it.

How will you decide if a given number is a triangular number?

Answer 1

To decide if a number is a triangular number:

1. Use the formula for the n-th triangular number: `T_n = (n(n+1))/2`
2. Solve the quadratic equation n² + n − 2T = 0, where T is the given number.
3. Check if the solution for n is a positive whole number (integer). If yes, the number is triangular.

Alternatively, you can check if 8T + 1 is a perfect square. If it is, the number T is triangular.