Let U1, U2,... be a sequence of independent uniform (0,1) random variables. In Example 5i,...

Let U1, U2,... be a sequence of independent uniform (0,1) random variables. In Example 5i, we showed that for , where

This problem gives another approach to establishing that result.

(a) Show by induction on n that for  and all ,

Use part (a) to conclude that