Series question

Printable View

• Apr 21st 2008, 08:51 AM
akhayoon
Series question
$\displaystyle \sum(-1)^{n}\frac{1+n}{n^{2}-n}$

in the sum n=2 and goes to infinity

so is the sequence divergent, conditionally convergent or absolutely convergent?

so I chose conditionally convergent because of the (-1)^n

but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?
• Apr 21st 2008, 09:55 AM
flyingsquirrel
Hi

The limit comparison test only apply for series with positive terms, the only things you might get is that $\displaystyle \sum \frac{1+n}{n^2-n}$ is divergent.

Quote:

so I chose conditionally convergent because of the (-1)^n
It's not because there is $\displaystyle (-1)^n$ that the series satisfy the alternating test. (you also need to show that $\displaystyle \frac{1+n}{n^2-n}$ decreases and that $\displaystyle \lim_{n\to \infty}\frac{1+n}{n^2-n}=0$)
• Apr 21st 2008, 11:59 AM
Mathstud28
Quote:

Originally Posted by akhayoon
$\displaystyle \sum(-1)^{n}\frac{1+n}{n^{2}-n}$

in the sum n=2 and goes to infinity

so is the sequence divergent, conditionally convergent or absolutely convergent?

so I chose conditionally convergent because of the (-1)^n

but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?

Two words...Ratio test (Cool)