# Thread: Is this alternating series divergent?

1. ## Is this alternating series divergent?

$\sum (2n+3)(-1)^n/(7n+11)$

Because it is neither decreasing, nor does it have a limit of 0?

2. Originally Posted by Mattpd
$\sum (2n+3)(-1)^n/(7n+11)$

Because it is neither decreasing, nor does it have a limit of 0?
see the complete explanation in this link ...

http://www.math.ucdavis.edu/~saito/courses/21C.s09/alternatingseriestest.pdf

3. Originally Posted by skeeter
So it's convergent? I was told it was divergent, and I am just here to double check...

Wouldn't you just look at everything but the (-1)^n part, and see that you have $(2n+3)/(7n+11)$ and because the powers of n are the same, the limit will be the ratio of the terms, which is 2/7, which is not 0, therefore it can't converge?

4. Originally Posted by Mattpd
So it's convergent? I was told it was divergent, and I am just here to double check...

Wouldn't you just look at everything but the (-1)^n part, and see that you have $(2n+3)/(7n+11)$ and because the powers of n are the same, the limit will be the ratio of the terms, which is 2/7, which is not 0, therefore it can't converge?
no ... it's divergent. did you read the article?

5. Originally Posted by skeeter
no ... it's divergent. did you read the article?
I did. I guess we were taught slightly wrong, because my notes say that if it fails any test, it is automatically divergent. Thank you for checking though.