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This should become clearer if we write the triangular numbers like this:
\begin{align*}
1 \amp = 1\\
3 \amp = 1+2\\
6 \amp = 1 + 2 + 3\\
10 \amp = 1+2 + 3+ 4\\
\vdots \amp \qquad \vdots\\
T_n \amp = 1 + 2 + 3 + \cdots + n\text{.}
\end{align*}
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