$X$ is a discrete random variable taking on the values $X=1,3,3^2,3^3,\ldots,3^m$ and $f(x)=P(X=x)=c / x$ for a constant $c$. Find $c$.
Solution: Since $P(X)=1$, we know that $cx=1$, so $c=x$. To find $x$, we have $x=\sum_{k=0}^m 3^m$. Since this series summation diverges to infinity, $c=∞$. This is a fascinating problem, however, something doesn't seem right ... in other words, how can $x=∞$? Is the first statement $c=x$ incorrect? Any help is greatly appreciated