# X have mass function For what values of α is it the case that E(X^α)

Let X have mass function
$f(x) = \left\{ \begin{array}{l l} \{x(x+1)\}^{-1} & \quad \text{if x = 1, 2, ...,}\\ 0 & \quad \text{otherwise,} \end{array} \right$

and let α∈R. For what values of α is it the case that E(X^α)<∞ ?
Can u please help I am dumbstruck from where to start
α<1/2

α<1

α>1

α<3/4