Closed Form for Triangular Numbers/Proof by Arithmetic Sequence

Theorem
The closed-form expression for the $n$th triangular number is:
 * $\displaystyle T_n = \sum_{i \mathop = 1}^n i = \frac {n \left({n+1}\right)} 2$

Proof
Follows directly from Sum of Arithmetic Progression putting $a = 1$ and $d = 1$.