Is the sequence $\{\frac {(-1)^n}{2n}\}$ convergent? If so, what is the limit?

Question

It is an exercise question in my textbook.

Question: Is the sequence $\{\frac {(-1)^n}{2n}\}$ convergent? If so, what is the limit? $|\{\frac {(-1)^n}{2n}\}-0|=|\{\frac {(-1)^n}{2n}\}| < \varepsilon$

I don't know what to do from here. Could you give some hint??

Answer 1

Hint: $\displaystyle(\forall n\in\mathbb{N}):-\frac1{2n}\leqslant\frac{(-1)^n}{2n}\leqslant\frac1{2n}$.

Answer 2

Use that $$\left|\frac{(-1)^n}{2n}\right|\le \frac{1}{2n}$$ and $$\frac{1}{2n}$$ tends to zero if $n$ tends to infinity.