1. If ∑an with an >0 is convergent, then is ∑an² always convergent? Either prove it or give a counterexample?

2. If ∑an with an >0 is convergent, then is ∑(anan+1)^(1/2) always convergent? Either prove it or give a counterexample?

3. Show that if a series is conditionally convergent, then the series obtained from its positive terms is divergent, and the series obtained from its negative terms is divergent.

Thanks