I am trying to find the limit of this sequence: $\displaystyle s_n = \dfrac{sin (n)}{n}. $ Any help would be appreciated.
For that limit you have to use the following theorem:
If $\displaystyle lim_{n\to\infty} x_{n} = 0$ and the sequence $\displaystyle y_{n}$ is bounded ,then $\displaystyle lim_{n\to\infty} x_{n}y_{n}=0$.
And in our case :
$\displaystyle y_{n} = sin(n)$ where $\displaystyle |sin(n)|\leq 1$ for all n ,and
$\displaystyle x_{n} =\frac{1}{n}$,where $\displaystyle lim_{n\to\infty}\frac{1}{n}=0$
Hence $\displaystyle lim_{n\to\infty}\frac{sin(n)}{n} = 0$