R'enyi's representation: the maximum of $n$ unit exponentials equals $\sum X_i/i$ in law

Let $X_1,X_2,\dots,X_n$ be independent rvs with exponential distribution having mean one. Define $Z=\max(X_1,\dots,X_n)$ and $W=X_1+\frac{X_2}2+\frac{X_3}3+\dots+\frac{X_n}n$. Then: