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

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- Jan 14th 2009, 06:57 AMMilly_BristolLimits - Degree Level Analysis
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 - Jan 14th 2009, 07:02 AMjames_bond
$\displaystyle \frac {2n}{n^3+1}=\frac {\frac 2{n^2}}{1+\frac 1{n^3}}$

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