# 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).

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