# Math Help - Prove or disprove sequences

1. ## Prove or disprove sequences

1. If the sequence {an^2} converges, then the sequence {an} also converges.

Is this true or false?
I think it is true because if {an^2} converges to a number a^2, i.e. |an^2-a^2| < e, then {an}will converge to a,which is the square root of a^2?

Any suggestions or corrections?

2. The sequence $a_{n}= (-1)^{n}$ doesn't converge... its square $a_{n}^{2}=1$ ? ...

3. Originally Posted by chisigma
The sequence $a_{n}= (-1)^{n}$ doesn't converge... its square $a_{n}^{2}=1$ ? ...
so an^2 converges and we have a contradiction..