# How do you test the series Sigma n/(n+4) from n is [0,oo) for convergence?

May 16, 2017

${\sum}_{n = 0}^{\infty} \frac{n}{n + 4} = \infty$

#### Explanation:

A necessary condition for any series $\sum {a}_{n}$ to converge is that:

${\lim}_{n \to \infty} {a}_{n} = 0$

In our case:

${\lim}_{n \to \infty} \frac{n}{n + 4} = 1$

so the series is not convergent.

As:

$\frac{n}{n + 4} > 0$

then the series is divergent.