This question already has an answer here:
Let $X$ be a discrete random variable, then $\mathbb{E}[X]=\sum_{n=1}^{\infty}\mathbb{P}(X \geq n)$
Is this true or false ?
I think it's false , just by using the definition of $\mathbb{E}[X]=\sum_{n=1}^{\infty}x_n\mathbb{P}(X=x_n)$. But I'm not so sure, it seems to be so trivial. I'd like to find a counter-example