How to find the minimum value of cos(2x)+cos(4x)+cos(6x)+cos(8x)+...+cos(20x) I want to find the minimum value of the series cos(2x)+cos(4x)+cos(6x)+cos(8x)+...+cos(2nx). x could be 2pit. Anyone can share a method of how to determine the minimum value of the series?

You can use
$\displaystyle \sum_{k=1} \cos(kx)=R\left(\sum_{k=1} e^{2ikx}\right)$
