# Thread: determine if series is absolutely convergent conditionally convergent or divergent

1. ## determine if series is absolutely convergent conditionally convergent or divergent

determine if series is absolutely convergent conditionally convergent or divergent

for sum from 1 to infinity of ((-1)^n)(n/(5+n))

my work: absolute value of lan+1/(an)l = (n+1/(5+(n+1))(5+n/(n)) as n goes to infinity equals 5/6 which is less than 1 so the series is absolutely convergent by ratio test.

is this right?

2. ... unfortunately that isn't right!...

In order to establish if the series...

$\sum_{n=1}^{\infty}(-1)^{n}\cdot \frac{n}{5+n}$

... converges you have invoked the ratio test. In your enthusiasm however you forgot to do a preliminary test which is necessary condition for convergence. What a test is that?...

Kind regards

$\chi$ $\sigma$

3. i still don't get where I went wrong

4. ## hi

Hi!

A necessary condition is that the terms go towards zero.

What is $\lim_{n \rightarrow \infty} \, \frac{n}{5+n}$ ?