Brain Teaser

Question

True or False?

The sum of two consective triangular numbers is always a square numbers!


Answer

Geometrically, a triangular number can be arranged as a staircase. Two consecutive triangular numbers would make two staircase shapes, where one staircase has one more step than the other, and the other smaller staircase can be flipped upside down and placed on top of the other to always form a square.

Therefore, it is true that the sum of two consecutive triangular numbers is always a square number.


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