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