HI everybody,

I must show that the following equation: cosx+cos2x+...+cosnx=0 $\displaystyle (n\in \mathbb{N}*)$ accepts at least one solution in $\displaystyle [0,\pi]$.

1)-We know that f(x)=cosx+cos2x+...+cosnx is continious in $\displaystyle [0,\pi]$.

2)-So i must show that $\displaystyle f(0)*f(\pi)<0$, BUT HOW?

CAN YOU HELP ME PLEASE?

AND THANKS ANYWAY.