I know that $m(t)=E[N(t)]$ for a Renewal process that has $N(t)$ arrivals.
I've seen at my class that there is a way of calculating $m(t)$ by doing $m(t)=\sum_{i=1}^\infty P(N(t)\geq i)$. But I also know that by the definition of Expectation: $E$, $m(t)=E[N(t)]=\sum_{i=1}^\infty P(N(t)=i) i$.
Where am I missing something to find that $P(N(t)\geq i)=P(N(t)=i)i$?