# Uniform boundedness

• December 16th 2009, 12:55 PM
skepticsmind
Uniform boundedness
Prove that the partial sums of $\sum$ cos nx are uniformly bounded. Note: Sorry I don't know laytex :(.

Attempt:

n/m, I've solved it.
• December 17th 2009, 05:46 PM
Jose27
Quote:

Originally Posted by skepticsmind
Prove that the partial sums of $\sum$ 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 $\mathbb{R}$ then taking $x=2\pi$ we get that $\sum \cos (nx) = \sum 1 = \infty$ so it can't be unif. (not even pointwise) bounded in the whole line.