I came across the following problem that says:
Let $x_{n}>0$ be such that $\sum_{2}^{\infty}x_{n}$ diverges and $\sum_{2}^{\infty}x_{n}^2$ converges. Then $x_n$ can not be which of the following?
$$ \begin{align}\frac{n}{n^{2}+1} \tag{a}\\ \frac{\log n}{n}\tag{b}\\ \frac{1}{n \sqrt {\log n}}\tag{c}\\\frac{1}{n(\log n)^{2}}\tag{d}\end{align}$$
Can someone point me in the right direction? Thanks in advance for your time.
