Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 9 / b / iv

The nonnegative integer-valued tail-sum formula for expectation givesThis is finite because $t-1>1$. Here $\zeta$ is the Riemann zeta function on its convergent real domain. The floor function is nonnegative on the support, so the tail-sum identity applies directly.