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

• Karl Porter

#### 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?

Karl Porter said:
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 ...

pbuk and berkeman