Question

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

Answer 1

`sum_(n=0)^oo n/(n+4) = oo`

Explanation:

A necessary condition for any series `sum a_n` to converge is that:

`lim_(n->oo) a_n = 0`

In our case:

`lim_(n->oo) n/(n+4) = 1`

so the series is not convergent.

As:

`n/(n+4) > 0`

then the series is divergent.