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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