Sum of Positive Integers

The yellow dots represent the value of $1 + 2 + 3 + 4 + \ldots + n$ and the blue dots represent the number $n+1$. If you hover over a yellow dot you see it is identified by exactly two blue dots. Conversely, any two blue dots uniquely identify a yellow dot. So this picture defines a bijection between $1 + 2 + 3 + 4 + \ldots + n$ and $\binom{n+1}{2}$. (There are $\binom{n+1}{2}$ different ways of choosing two blue dots ouf of $n+1$ dots.)

$\definecolor{colorOrange}{RGB}{255,165,0}\definecolor{colorPurple}{RGB}{138,43,226} \textcolor{colorOrange}{1 + 2 + 3 + 4 + \ldots + n} = \textcolor{colorPurple}{\binom{n + 1}{2}} $

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