# How do you determine whether the sequence a_n=(n+2)/n converges, if so how do you find the limit?

Feb 25, 2017

It coverages to unity..

#### Explanation:

We have the sequence $\left\{{a}_{n}\right\}$ where:

${a}_{n} = \frac{n + 2}{n}$
$\setminus \setminus \setminus \setminus = 1 + \frac{2}{n}$

And so as $n \rightarrow \infty \implies {a}_{n} \rightarrow 1$

NB: A common result is that the harmonic series ${\sum}_{r = 1}^{\infty} \frac{1}{r}$ diverges and hence the series ${\sum}_{r = 1}^{\infty} {a}_{r}$ diverges.

We can also visualise how the sequence behaves by looking at the graph of the function:

graph{(x+2)/x [-10, 10, -5, 5]}