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 αR. 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

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