I have a question but can't seem to figure out how to solve it. The problem states:
Let's consider a sequence $x_n$, such that $x_n\to a$, as $n \to \infty$. Using the Cauchy Principle prove that (a) if $x_n \geq 1$, then $(-1)^nx_n + 2x_n$ is divergent. (b) if $a = 0$, then $(-1)^nx_n + \frac1n$ is convergent.
I'd appreciate any help I can get. Thank you in advance.