prove real analysis series question: $\sum^{\infty}_{i=0}a_i^2b_i^2 < \infty $ [closed]

Suppose, $a_k$ and $b_k$ is non-negative sequences. $a_k$ decreasing, $\sum^{\infty}_{i=0}a_i $ diverge to $\infty$, and $\sum^{\infty}_{i=0}a_i^2$ converge.

For $\sum^{\infty}_{i=0}a_i^2b_i^2 < \infty$ to hold, what conditions must sequence $b_k$ satisfy?
My answer: $b_k$ it only need to be bounded sequence (not sure if it correct or how to prove). But this is not required for $b_k$, so what is?

(English not my language, please excuse.)