determine if series is absolutely convergent conditionally convergent or divergent

**twilightstr** · April 5th 2009, 08:27 PM

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?

**chisigma** · April 5th 2009, 10:26 PM

... 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

$\chi$ $\sigma$

**twilightstr** · April 6th 2009, 09:43 PM

i still don't get where I went wrong

**Twig** · April 6th 2009, 10:03 PM

Hi!

A necessary condition is that the terms go towards zero.

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

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determine if series is absolutely convergent conditionally convergent or divergent

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