Limits - Degree Level Analysis

Milly_Bristol · #1 $Old$ January 14th, 2009, 08:57 AM

Hi,
I'm trying to prove that 2n/(n^3+1) is a null sequence. I have done the modulus of this < epsilon.

Ended up with 2n < E(n^3+1)

Where do I go from here? I can't work out how to simplify it

james_bond · #2 $Old$ January 14th, 2009, 09:02 AM

$\frac {2n}{n^3+1}=\frac {\frac 2{n^2}}{1+\frac 1{n^3}}$
We know that (if you don't then you should try to prove it) $\lim_{n\rightarrow\infty}\frac 2{n^2}=0$ and $\lim_{n\rightarrow\infty}\frac 1{n^3}=0$ therefore $\lim_{n\rightarrow\infty}\frac {\frac 2{n^2}}{1+\frac 1{n^3}}=\frac 01=0$ .