How to show that $$ \sum_{n=2}^\infty \frac{\sin{(nx)}}{\log n} $$ not the Fourier series of any function?
I have shown that the series is convergent by Dirichlet test.
Let $a(n)=\frac{1}{\log n}$. What is $\sum (a(n))^2$, to apply Parseval's theorem?