Closed Form for Triangular Numbers/Also presented as

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Closed Form for Triangular Numbers: Also presented as

The closed-form expression for the $n$th triangular number can also be presented as:

$\ds T_n = \sum_{i \mathop = 0}^n i = \frac {n \paren {n + 1} } 2$

This is seen to be equivalent to the given form by the fact that the first term $T_0$ evaluates as $\dfrac {0 \paren {0 + 1} } 2$ which is zero.