T(n+1)^2-T(n)^2=(n+1)^3

Theorem

The following formula holds for $n=1,2,3,\ldots$: $$T(n+1)^2-T(n)^2=(n+1)^3,$$ where $T(n)$ denotes the $n$th triangular number.

References

• V.E. Hoggatt, Jr and Marjorie Bicknell: Triangular numbers (1974)... (previous)... (next) $(1.5)$