# converging, absolutely, conditionally or diverging.

• Jan 28th 2008, 10:41 PM
rcmango
converging, absolutely, conditionally or diverging.
here is the problem: http://img255.imageshack.us/img255/4224/54516302vs6.png

it completely looks like it would diverge.

could i use the direct comparison test to show that?

first it can't converge absolutely because the absolute value of the series is a divergent p series p <= 1 not meeting the standards of a p series.

also, could i compare this to the harmonic series and show that the original series in the pic, is actually larger than the harmonic series, showing that it diverges alltogether.

thanks.
• Jan 28th 2008, 11:09 PM
Jhevon
Quote:

Originally Posted by rcmango
here is the problem: http://img255.imageshack.us/img255/4224/54516302vs6.png

it completely looks like it would diverge.

could i use the direct comparison test to show that?

first it can't converge absolutely because the absolute value of the series is a divergent p series p <= 1 not meeting the standards of a p series.

also, could i compare this to the harmonic series and show that the original series in the pic, is actually larger than the harmonic series, showing that it diverges alltogether.

thanks.

it is not a p-series

use the alternating series test. that should be the first one you look at since you saw the (-1)^n

whenever you see (-1)^n, look at the alternating series test first
• Jan 29th 2008, 04:59 AM
curvature
Quote:

Originally Posted by rcmango
here is the problem: http://img255.imageshack.us/img255/4224/54516302vs6.png

it completely looks like it would diverge.

could i use the direct comparison test to show that?

first it can't converge absolutely because the absolute value of the series is a divergent p series p <= 1 not meeting the standards of a p series.

also, could i compare this to the harmonic series and show that the original series in the pic, is actually larger than the harmonic series, showing that it diverges alltogether.

thanks.

It diverges since the general term does not tends to zero.