1. The problem statement, all variables and given/known data Consider the infinite series ∞ ∑ (-1)n+1 cos(nx) n=1 Is there any convergence? (Answer: No convergence) 2. Relevant equations/concepts Infinite series 3. The attempt at a solution I was looking back in my 1st year calculus textbook, but none of the theorems seem to apply. Basic divergence test: If an does not converges to 0 as n->∞, then ∑ an diverges. [well...here the an's are constants and does not depend on x, so this theorem does not apply in our case] Secondly, it is not a power series (it has cos(nx) here), so none of the theorems about power series apply here. Can someone please explain why the above infinite series has no convergence? Thank you!