Why can a term be factored out of the numerator in a converging sequence?

[trap101]

State whether the sequence converges and if so, find the limit


(n+1)^1/2/2(n)^1/2

ok so I got that it converges to 1/2, my question more so lies in the fact that why are we able to factor out a (n)^1/2 from the term in the numerator? Isn't it only the denominator that we are concerned about when it comes to powers? or is it because the denominator is technically "factored" already?

 

[Mark44]

State whether the sequence converges and if so, find the limit


(n+1)^1/2/2(n)^1/2

ok so I got that it converges to 1/2, my question more so lies in the fact that why are we able to factor out a (n)^1/2 from the term in the numerator? Isn't it only the denominator that we are concerned about when it comes to powers?

No, you also need to look at the numerator.

or is it because the denominator is technically "factored" already?

 

[trap101]

ok. thanks