Let $U_1, U_2, \ldots$ be a sequence of independent random variables with PDF $f(u) = 1, \;\; 0 < u < 1$.
Find $E[N]$ for $N =\min\{n:U_1+U_2\cdots+U_n>1\}$ where $U_1,U_2, . . .$ are independent uniform (0,1) random variables.