As per my course requirement, I was reading a paper titled "Optimal Speed-up of Las Vegas Algorithm" by M. Luby et. al . I couldn't get around this Lemma
$$T(S) = \sum\limits_{t \leq t_{1}} t \cdot p(t) + (1 - q(t_{1})) \cdot (t_{1}) + T(S'))\\ \qquad = q(t_{1}) \cdot l(t_{1}) + (1 - q(t_{1})) \cdot T(S')\\$$ where $q(t) = \sum\limits_{t' \leq t} p(t')$ is a cumulative distribution function of $p$ ans $S = (t_{1},t_{2},t_{3},...)$ be any strategy and strategy $S' = (t_{2},t_{3},...)$ with $t_{1}$ is omitted.