Hi guys,

i need to prove or disprove these statements:

a. if the series $\displaystyle \sum a_{n}$ is convergent, then $\displaystyle \sum \frac{1}{a_{n}}$ is divergent.

a. if the positive series $\displaystyle \sum a_{n}$ is convergent, then $\displaystyle \sum a_{n}^2$ is convergent.

if the statement is false, i need an example of contradiction.

basically i can really use some tips about how to approach these questions;

what tests should i use to determine if a statment is true or false (or maybe the first step should be merely my intuition), and in what ways can i prove it?

thanks in advanced!