Part I. Sec. 4.2. Prove by mathematical induction that for all n?1
$\sum_{i=1}^{n} (3i) = \frac{3n(n+1)}{2}$
Part II. Sec. 4.4. Consider the alphabet {x,y,z}. Let $r_n$ be the number of words of length
n in this alphabet that do not contain "xz" in them.
i) Calculate $r_0$, $r_1$, and $r_2$.
ii) Find a recurrence formula for $r_n$