if $b_j>0$ and $\sum b_j$ converges . prove that $\sum \frac{\sqrt{b_j}}{j^\alpha}$ converge for $\alpha>1/2$.

Question

$b_j>0$ and $\sum b_j$ converges . prove that $\sum \frac{\sqrt{b_j}}{j^\alpha}$ converge for $\alpha>1/2$.

I know that $\sum \sqrt{b_j}$ and $\sum \frac{1}{j^{2\alpha}}$ converge. O just don't know how to proceed from there.