Converge, absolutely or conditionally?

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Homework Help Overview

The discussion revolves around the convergence properties of a series involving the sine function, specifically whether it converges absolutely, conditionally, or diverges. The original poster presents an equation and expresses uncertainty regarding the nature of convergence, particularly in the context of an alternating series.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the behavior of the sine function as the variable approaches zero and discuss the implications for convergence. Questions arise about the conditions necessary for an alternating series to converge and the specific behavior of the sine function at certain values.

Discussion Status

Some participants have offered insights regarding the convergence of the series, while others are questioning the assumptions about the sine function's behavior. Multiple interpretations of the convergence criteria are being explored, indicating an active discussion without a clear consensus.

Contextual Notes

There is uncertainty regarding the specific conditions under which the sine function converges to zero, as well as the implications of the series being alternating. The original poster's reference to the sine function's behavior at various inputs is also under scrutiny.

rcmango
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Homework Statement



does it converge absolutely, converge conditionally, or diverge?

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

Homework Equations



sin(pi/n)

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:
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Yep, The terms converge to zero, and it converges absolutely, and therefore also with the alternating series.
 
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:
Ahh no, if anything was a constant that it won't be zero.
 
rcmango said:
..and, in this problem, sin(pi/anything) will always be 0, correct?

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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