If $\sum a_n$ converges, then $\sum \frac{1}{a_n}$ diverges to $\infty$
If $\sum a_n$ diverges, then for every $M > 0$ $\exists$ $n$ such that $s_n > M$
^ Are the statements above true? I'm not given any information about $a_n$, which is a series. $s_n$ denotes a partial sum of the series. I have no idea about the second one, but for the first one I'm pretty sure you can assume that any series that converges will not have its reciprocal converge, for example $\frac{1}{x^2}$ converges, but $x^2$ does not. The second one seems to be a question about whether there's a limit to the sequence, and again I have no idea how to do.