Limit of a Sequence: Does Square or Sqrt Change It?

[Karl Porter]

Homework Statement

I was curious, if I have a sequence that has a limit of 1

Relevant Equations

Lim an=1 as n tends to inf
Lim of an^2=1 as n tends to inf

Does the square of the sequence also have a limit of 1. Does the square root also equal 1? I've been trying to find some counterexamples but I think the limit doesn't change under these operations?

 

[PeroK]

Homework Statement:: I was curious, if I have a sequence that has a limit of 1
Relevant Equations:: Lim an=1 as n tends to inf
Lim of an^2=1 as n tends to inf

Does the square of the sequence also have a limit of 1. Does the square root also equal 1? I've been trying to find some counterexamples but I think the limit doesn't change under these operations?

Can you think of a basic theorem of limits that would lead to a one line proof?

Hint: If $\lim_{n \rightarrow \infty} a_n = L_a$ and $\lim_{n \rightarrow \infty} b_n = L_b$, then ...