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## Homework Statement

Show by example that if Ʃa

_{n}and Ʃb

_{n}are two convergent series, then Ʃ (a

_{n}b

_{n}) may be a divergent series.

## Homework Equations

N/A

## The Attempt at a Solution

I've been trying long and hard to find an example for this particular case, but I'm unable to find one. I've found examples where Ʃa

_{n}and Ʃb

_{n}are divergent, but Ʃ(a

_{n}b

_{n}) is convergent. Can anyone please give an example? Thanks.