1. (5 marks). In this question, we'll consider the series
$$sum_{n=1}^{infty} (ln(n + 1) - ln(n)).$$
(a) Let $a_n = ln(n + 1) - ln(n)$. Does the sequence ${a_n}_{n=1}^{infty}$ converge or diverge?
(b) Let $S_N$ be the $N$th partial sum of the series, that is
$$S_N = sum_{n=1}^N (ln(n + 1) - ln(n)).$$
Simplify this expression for $S_N$ as much as possible by rewriting the expression for $S_N$ without sigma notation (i.e. expand the sum).
(c) Use your expression for $S_N$ from (b) to show that this series diverges. Could you have also concluded this from the Test for Divergence?