Putnam 2020 B3

Let $x_0 = 1$, and let $\delta$ be some constant satisfying $0 < \delta < 1$. Iteratively, for $n=0,1,2,\dots$, a point $x_{n+1}$ is chosen uniformly from the interval $[0, x_n]$. Let $Z$ be the smallest value of $n$ for which $x_n < \delta$. Find the expected value of $Z$, as a function of $\delta$.