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'Triangle Numbers' printed from http://nrich.maths.org/

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The first triangle number is $1$
The second triangle number is $1 + 2$
The third triangle number is $1 + 2 + 3$
The fourth triangle number is $1 + 2 + 3 + 4 \ldots$

The $n^{\text{th}}$ triangle number is $\frac{n(n+1)}{2}$