Converge, absolutely or conditionally?

1. Jan 24, 2007

rcmango

1. The problem statement, all variables and given/known data

does it converge absolutely, converge conditionally, or diverge?

heres the equation: http://img219.imageshack.us/img219/4645/untitled29fy.jpg [Broken]

2. Relevant equations

sin(pi/n)

3. The attempt at a solution

looks like the sin equation converges to zero.

i think this is an alternating series, but i'm not sure if this part converges or diverges?

thanks for any help here.

Last edited by a moderator: May 2, 2017
2. Jan 24, 2007

Gib Z

Yep, The terms converge to zero, and it converges absolutely, and therfore also with the alternating series.

3. Jan 24, 2007

rcmango

Great, thanks again.

..also, the alternating series must approach 0, in order to converge right?

..and, in this problem, sin(pi/anything) will always be 0, correct?

Last edited: Jan 24, 2007
4. Jan 24, 2007

Gib Z

Ahh no, if anything was a constant that it wont be zero.

5. Jan 24, 2007

AlephZero

No ... but sin(pi*n) is always 0 when n is an integer. Maybe that's what you were thinking of (though it doesn't seem relevant to this question).