1. The problem is if an is convergent then prove or disprove by giving a counter example that an2 is also convergent. 2. Since an is convergent then for all ε>0 there exists n0[itex]\in[/itex] [itex]N[/itex] such that lan-Ll<ε for all n>=n0 So I then tried squaring (an-L) which gives an2 -2anL +L2<ε2 How do I manipulate this to show that an2 has a limit L too? Or should I be looking for a counter example? I can't think of any!