JEE Advance - Mathematics (1997 - No. 10)
Prove that $$\sum\limits_{k = 1}^{n - 1} {\left( {n - k} \right)\,\cos \,{{2k\pi } \over n} = - {n \over 2},} $$ where $$n \ge 3$$ is an integer.
The statement is true and can be proven using complex numbers and geometric series.
The statement is false for all n >= 3.
The statement is only true for even values of n.
The statement is only true for prime values of n.
The statement is true but requires advanced knowledge of Fourier analysis to prove.