Expected largest value and spread of n uniforms

Draw $n$ independent random numbers, each uniform on $[0,1]$. What is the expected value of the largest one? What is the expected difference between the largest and the smallest?

$\tfrac{n}{n+1}$ and $\tfrac{n-1}{n+1}$. The maximum has CDF $x^n$, so $\mathbb{E}[\max]=\int_0^1(1-x^n)\,dx=\tfrac{n}{n+1}$. By symmetry $\mathbb{E}[\min]=\tfrac1{n+1}$, and the expected range is the difference.