Let $p$ be the function from $\mathbb { R }$ to $\mathbb { R }$ defined by $$p ( x ) = \sum _ { n = 1 } ^ { + \infty } \frac { \cos ( n x ) } { n \sqrt { n } }$$ Show that $p$ is well defined, continuous and $2 \pi$-periodic.
Let $p$ be the function from $\mathbb { R }$ to $\mathbb { R }$ defined by
$$p ( x ) = \sum _ { n = 1 } ^ { + \infty } \frac { \cos ( n x ) } { n \sqrt { n } }$$
Show that $p$ is well defined, continuous and $2 \pi$-periodic.