# How do you determine whether the infinite sequence a_n=(2n)/(n+1) converges or diverges?

${\lim}_{n \to \infty} {a}_{n} = {\lim}_{n \to \infty} \frac{2 n}{n + 1}$
$= {\lim}_{n \to \infty} \frac{2 n}{n + 1} \cdot \frac{\frac{1}{n}}{\frac{1}{n}}$
$= {\lim}_{n \to \infty} \frac{2}{1 + \frac{1}{n}} = \frac{2}{1 + 0} = 2$
Hence, the sequence $\left\{{a}_{n}\right\}$ converges to $2$.