Whether the series converges or diverges

Question

The series is given as $$\sum_1^\infty\left(\frac{1}{n^2}+\frac{1}{n}\right)$$ In the answer the given series diverges. But I don't know how. Also tell me how $\sum_1^\infty\frac{1}{n}$ diverges.

Answer 1

Since general term $$\dfrac{1}{n^2}+\dfrac{1}{n}=\dfrac{1+n}{n^2}\sim \dfrac{1}{n}$$ but $$\sum\limits_{n\leqslant N} \dfrac{1}{n}\sim \ln N$$ so initial series diverges