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

[Frogeyedpeas]

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

 

[lugita15]

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.