Which of the following statements about the function f(x)=∑n=1∞cos(nx)n2f(x) = \sum_{n=1}^{\infty} \frac{\cos(nx)}{n^2}f(x)=∑n=1∞n2cos(nx) is/are correct?
The series converges uniformly on all of R\mathbb{R}R and fff is continuous everywhere.
The series converges only for x∈(−π,π)x \in (-\pi, \pi)x∈(−π,π) and does not converge at the endpoints.
Uniform convergence fails at x=0x = 0x=0, so term-by-term differentiation is not valid.
The series converges absolutely on R\mathbb{R}R and is differentiable with f′(x)=−∑n=1∞sin(nx)nf'(x) = -\sum_{n=1}^{\infty} \frac{\sin(nx)}{n}f′(x)=−∑n=1∞nsin(nx).