Originally Posted by

**mremwo** I am so confused with Cauchy Sequences. I was sick the day we learned about them. Here are two problems that I am absolutely unsure about. (just two of many)

1. Prove straight from the definition that $\displaystyle (n + \frac{(-1)^n}{n})$ is NOT a Cauchy Sequences

and

2. Let $\displaystyle (x_{n})$ be a Cauchy Sequence such that $\displaystyle x_{n}$ is an integer for every $\displaystyle n \in N$. Show that $\displaystyle (x_{n})$ is ultimately constant.

As I said, I am so lost. Please help? Thanks so much.