\begin{aligned} \sum xP(X=x) & = \sum x \cdot \frac{1}{n} \\ & = \frac{1}{n} \left( \frac{1}{n} + \frac{2}{n} + \ldots + \frac{n}{n} \right) \\ & = \frac{1}{n^2} (1+2+ \ldots + n)
\begin{aligned} \sum xP(X=x) & = \sum x \cdot \frac{1}{n} \\ & = \frac{1}{n} \left( \frac{1}{n} + \frac{2}{n} + \ldots + \frac{n}{n} \right) \\ & = \frac{1}{n^2} (1+2+ \ldots + n)
\begin{aligned} \sum xP(X=x) & = \sum x \cdot \frac{1}{n} \\ & = \frac{1}{n} \left( \frac{1}{n} + \frac{2}{n} + \ldots + \frac{n}{n} \right) \\ & = \frac{1}{n^2} (1+2+ \ldots + n)
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