$\sum_{n=2}^\infty \frac{e^{2\pi in t}}{n \log n}$

Question

Does any know how to show that $\sum_{n=2}^\infty \frac{e^{2\pi in t}}{n \log n}$ is in $L^{2}(\mathbb T)$

Answer 1

Hint: this is equivalent to showing that $\sum_{n=2}^\infty\frac{1}{n^2 \log^2 n} < \infty.$