Prove that the partial sums of $\displaystyle \sum$ cos nx are uniformly bounded. Note: Sorry I don't know laytex .
Attempt:
n/m, I've solved it.
Is this really unif. bounded? In which interval? If you work in $\displaystyle \mathbb{R}$ then taking $\displaystyle x=2\pi$ we get that $\displaystyle \sum \cos (nx) = \sum 1 = \infty$ so it can't be unif. (not even pointwise) bounded in the whole line.