Let $\left(x_{n}\right)_{n=1}^{\infty}$ be a sequence of real numbers. What does it mean to say that the sequence $\left(x_{n}\right)$ is convergent? What does it mean to say the series $\sum x_{n}$ is convergent? Show that if $\sum x_{n}$ is convergent, then the sequence $\left(x_{n}\right)$ converges to zero. Show that the converse is not necessarily true.