Using R2482: Expectation of discrete random variable, one has \begin{equation} \begin{split} \mathbb{E} X^n & = 1^n \cdot \mathbb{P}(X = 1) + 0^n \cdot \mathbb{P}(X = 0) \\ & = 1^n \theta \\ & = \theta \end{split} \end{equation} $\square$