The p.m.f. of a random variable X is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, ....... n \\ 0, & \text{otherwise} \end{cases}$, then $E(X)$ is
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The expected value of a discrete random variable is the sum of each possible value multiplied by its probability. Remember the formula for the sum of the first $n$ squares: $\sum_{x=1}^{n} x^2 = \frac{n(n+1)(2n+1)}{6}$.