calculus - $sum_{n=2}^{infty} frac{1}{n log n}$ Prove series diverge using comparsion test .

prove

$$\sum_{n=2}^{\infty} \frac{1}{n \log n}$$ diverge. I have done this problem using cauchy integral test and condensation test. But i want to do it by comparison test or by limit comparison test . any hint about that .

Thanks in advanced.