1. Show that for all m < n E N and all 2 < k < n E N, \frac{1}{m^{k}}\left(\begin{array}{c} m \\ k \end{array}\right)<\frac{1}{n^{k}}\left(\begin{array}{l} n \\ k \end{array}\right) \leq \frac{1}{k

!} 2. Use the binomial theorem to show that a_{n}:=\left(1+\frac{1}{n}\right)^{n} is a strictly monotone increasing sequence.