Let $X$ be a discrete random variable with finite expectation. Show that $$\mathbb{E}\left(X \mathbb{1}_{|X| \leqslant C}\right) \xrightarrow{C \rightarrow +\infty} \mathbb{E}(X).$$
Let $X$ be a discrete random variable with finite expectation. Show that
$$\mathbb{E}\left(X \mathbb{1}_{|X| \leqslant C}\right) \xrightarrow{C \rightarrow +\infty} \mathbb{E}(X).$$