limit of a sequence $\frac{(-1)^n}{n}$

Question

Finding Convergence or divergence of sequence $$a_{n}=\frac{2+(-1)^n}{n}$$

What I try :: A sequence $\{a_{n}\}$ is convergent

if $\displaystyle \lim_{n\rightarrow \infty}a_{n}=0.$ Otherwise it is diverges.

$$\lim_{n\rightarrow \infty}a_{n}=\lim_{n\rightarrow \infty}\frac{2+(-1)^n}{n}=0+\lim_{n\rightarrow \infty}\frac{(-1)^n}{n}$$

Can anyone please tell me how can I solve that limit. Help me please

Answer 1

Hint - By the triangle inequality, $|a_{n}|\le \frac{3}{n}$.

Answer 2

Use that $$\left|\frac{(-1)^n}{n}\right|\le \frac{1}{n}$$