Question

Limit question

Answer 1

One of the limit laws states:
\(\lim_{x \rightarrow \infty}\frac{ ax^b }{ cx^b } = \frac{ a }{ c }\) where be is a constant

but I just got the problem:
"State whether the sequence:
\[a _{n}=\frac{ 2^n }{ 4^n+2 }\]
converges, and if it does find the limit.
n is technically going to be a constant here, why wouldnt this limit law be applied to this problem? (I got the question wrong and answered lim = 1/2)

Answer 2

comparison test?

Answer 3

Might help a little, possibly\[\large a _{n}=\frac{ 2^n }{ 4^n+2 } =\frac{ 2^n }{ 2^{2n}+2 }\]