Question

How does the reasoning behind this limit work?

Answer 1

\[\lim_{n \rightarrow +\infty}\frac{ 2^{n}+n }{ 2^{n+1} }=\frac{ \infty }{ \infty }\]

Answer 2

\[2^{n}+n=2^{n}(1+ \frac{ n }{ 2^{n} })\approx2^{n}\]

Answer 3

since \[\frac{ n }{ 2^{n} }\rightarrow0\] and\[(1+\frac{ n }{ 2^{n} })\rightarrow1\]

Answer 4

It means that \[\frac{ 2^{n}+n }{ 2^{n+1} }\approx \frac{ 2^{n} }{ 2^{n+1} }=\frac{ 1 }{ 2 }\]

Answer 5

I used that symbol in order to indicate that the fraction is asymptotic to a certain number. I couldn'tfind the right symbol so I just had to use this one instead: \[\approx\]