Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

(2/5) + (2 x 6 / 5 x 8) + ( 2 x 6 x 10 / 5 x 8 x 11) + ....

I'm having a lot of trouble with this. I don't know where to start...

Take out the common factors and you get:

(2/5)( 1 + (6/8)( 1 + (10/11)( 1 + ...

assuming the common factor ratios will continue approaching 1 the series will be divergent

edit: Actually it's even better than that, if the apparent trend of adding 4 to the numerator and 3 to the denominator for each new factor continues, all of the following factors will be greater than 1 and the terms will start to actually grow.

edit2: I'm not sure what the other answer is trying to say but a decreasing series can be divergent as long as it's decreasing slower or at the same rate as the harmonic series (1+1/2+1/3+1/4+...).

First, you should decide the format the series takes.

Your first term is (2/5). Let's call this a1.

Your second term is (2 x 6 / 5 * 8) so a2 = 12/40 = 3/10,

Your third term (a3) = 120/440 = 3/11.

Okay, so we can see that this series is decreasing as we approach an infinite sum. Eventually, we will reach a number so small that it is almost zero. Therefore, it is absolutely convergent because we can add all the numbers together to find the sum of the series. In other words (sigma) sum from n=0 to infinity of |an| = a number not equal to infinity

A conditionally convergent sum is one where the sum as |an| from n = 0 to infinity = infinity.