Problem 1. Prove that if $r > 1$, then the sequence $(1, r, r^2, r^3, r^4, ...)$ is unbounded. Deduce that this sequence does not converge when $r > 1$. (Hint: the binomial theorem states that $(1 + x)^n = \sum_{k=0}^n \binom{n}{k} x^k$ where $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ are the binomial coefficients. Use this theorem to prove that $(1 + x)^n \ge 1 + nx$. Now let $x = r - 1$.)
