Question

Represent Triangular Numbers By Adding Two Consecutive Triangular Numbers​

Answer 1

Answer:

The difference between the squares of those two consecutive triangular numbers is equal to a cube. The sum of those four cubes is equal to the square of the fourth triangle. Alternatively, since every square number is the sum of consecutive odd numbers, so is the square of a triangular number.

Answer 2

Triangular numbers are obtained by continued summation of natural numbers 1,2,3,4,5,6,7

∴ Set of triangular numbers is 1,3,6,10,15,21,28

When we add two triangular numbers we get a perfect square number

For example, 1+3=4=2${}^{2}$,3+6=9=

3${}^{2}$ , 6+10=16=4${}^{2}$ and so on..