sum and product of cos

\hspace{-16}\bf{\sum_{n=1}^{\infty}\;\prod_{r=1}^{n}\cos \left(\frac{r\pi}{n}\right)}

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9
souradipta Sen ·

Πcos(rπn)
=cos(πn)cos(2πn)cos(3πn).......cos(nπn)
=2sin(πn)cos(πn)cos(2πn)cos(3πn).......cos(nπn)2sin(πn)
=sin2Ï€2nsin(Ï€n)=0

ΣΠcos(rπn)=0

i am not sure but i think so

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