Show that $p(n)=\frac1{n(n+1)}$ for $n = 1, 2,...$ is a probability function for some discrete random variable $X$. Find $E(X)$.
So I know that $E(X)$ for a discrete random variable is $E(X)=x1p1+x2p2+...$ if $X$ is a discrete random variable that takes values $x1,x2,...$ with corresponding probabilities $p1,p2,..$. For this question is $p(n)$ the probability for any value of $n$? For example $p(1)=\frac1{2}$ and this would be the probability for x1? If this is true how would you go about proving that p(n) is a probability function? I assume once this is proven I can use the above equation to find $E(X)$? Am I close?