# Prove or disprove if a series is convergent that it implies the square of the series is convergent as well

Heyy,

Can we prove or disprove the following

$$\Sigma a_n \text{ is convergent} \Rightarrow \Sigma a_n^2 \text{ is convergent}$$

Since the statement cannot be proven without knowing whether the series is positive, is there a proper counter example

Thank You

$$a_n:=\frac{(-1)^n}{\sqrt n}$$
This is false. Consider $\sum \frac{(-1)^n}{\sqrt{n}}$.