We consider the function series $\sum _ { n \geq 1 } \frac { \sin ( n x ) } { \sqrt { n } }$, where $x$ is a real variable. Show that this function series converges pointwise on $\mathbb { R }$.
We consider the function series $\sum _ { n \geq 1 } \frac { \sin ( n x ) } { \sqrt { n } }$, where $x$ is a real variable.
Show that this function series converges pointwise on $\mathbb { R }$.