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## Homework Statement

Find [tex]a_n[/tex] & [tex]b_n[/tex] such that [tex]\sum_{n=0}^{\infty}a_n[/tex] & [tex]\sum_{n=0}^{\infty}b_n[/tex] are convergent series, but [tex]\displaystyle \sum_{n=0}^{\infty} \left( \sqrt{a_n} \cdot b_n \right)[/tex] diverges.

## Homework Equations

None.

## The Attempt at a Solution

Try too hard for this but still cannot find such [tex]a_n[/tex] & [tex]b_n[/tex].