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...

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

... 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

$\displaystyle \chi$ $\displaystyle \sigma$

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

Search Tags

absolutely, conditionally, convergent, determine, divergent, series 