A possible solution to the infinite summation of sin(x)

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The discussion centers on the convergence of the infinite summation of sin(πnx) defined by P(x) over the interval [-2π, 2π]. The contributor posits that this series may converge to a function resembling the tangent function. Observations indicate that the partial sums oscillate without approaching a definitive value, except at x=0. This suggests a complex behavior of the series that warrants further mathematical exploration.

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Frogeyedpeas
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So basically here's the deal:

I believe there exists a P(x) defined on [-2π, 2π]

such that over that interval P(x) = \sum^{\infty}_{n=0}[sin(πnx)]

Its weird but I have a feeling that this might converge to a function such as tangent
 
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See here. You can see that the formula for the partial sum just oscilllates and doesn't approach any value as you go to infinity, except for x=0.
 

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