# determine if series is absolutely convergent conditionally convergent or divergent

• Apr 5th 2009, 08:27 PM
twilightstr
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?
• Apr 5th 2009, 10:26 PM
chisigma
... unfortunately that isn't right!(Shake)...

In order to establish if the series...

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

... 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

$\displaystyle \chi$ $\displaystyle \sigma$
• Apr 6th 2009, 09:43 PM
twilightstr
i still don't get where I went wrong
• Apr 6th 2009, 10:03 PM
Twig
hi
Hi!

A necessary condition is that the terms go towards zero.

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