T(n)=n(n+1)/2
From specialfunctionswiki
Theorem
The following formula holds for all $n=1,2,3,\ldots$: $$T(n)=\dfrac{n(n+1)}{2},$$ where $T(n)$ denotes the $n$th triangular number.
Proof
References
- V.E. Hoggatt, Jr and Marjorie Bicknell: Triangular numbers (1974)... (previous)... (next) $(1.1)$
