Square Numbers and Triangular Numbers Prove that the sum of two consecutive…

MATHEMATICS · Subjective · A Level · Mathematics · Proof · Proof

Problem

51. Square Numbers and Triangular Numbers Prove that the sum of two consecutive triangular numbers is a square number; that is, prove

T_{n-1}+T_{n}=n^{2}

for all positive integers

n \geq 2

. Use both a geometric and an algebraic approach.