The Question: Is it possible to find a sequence $(a_n)$ such that $\sum_{n =1}^{\infty} {a_n}^{2}$ converges however $\sum_{n=1}^{\infty} \frac{a_n^{2}}{n}$ diverges.
I am having a hard time coming up with examples. I am guessing we have to use terms with $ln(x)$ in it. Are there any examples?
Thank you very much!!
No because $$\sum_n\frac{a_n^2}{n} \leq \sum_na_n^2<\infty$$