Hi,

$\displaystyle \rm{1.\ Prove\ by\ induction\ that\ 3^n \geq 1 + 2^n\ for\ all\ positive\ integers\ n.}$

A hint or two may suffice with this one.

$\displaystyle \rm{2.\ Show\ that\ all\ arithmetic\ progressions\ are\ divergent.}$

For any arithmetic progression, $\displaystyle \displaystyle S_n = \frac{n}{2}(2a + (n - 1)d),$ which always approaches infinity as $\displaystyle n \rightarrow \infty$.

Therefore any AP is divergent.