How to Verify Big O Notation for (n^2 + 3n - 3)/n^3 = 0 + O(2/n)

[JazzRun]

Homework Statement

Verify that (n^2 + 3n -3)/n^3 = 0 + O(2/n)

Homework Equations

The Attempt at a Solution

I really don't have an attempt. I understand Big O notation, but I don't know how to verify this.

 

[micromass]

What does the big O notation mean?

 

[JazzRun]

a_n converges to A with a rate of convergence O(b_n). Then you can write a_n=A + O(b_n)

 

[micromass]

a_n converges to A with a rate of convergence O(b_n). Then you can write a_n=A + O(b_n)

You still didn't say what "converging with a rate of convergence $O(b_n)$" means.

 

[JazzRun]

I'm not sure, that's why I'm asking :(

 

[Muphrid]

Big O notation tells you about the leading (that is, largest, or most significant or dominant) contribution to the rate of convergence. Often, the rate of convergence is a sum of terms of the form $n^a$ for some number $a$. The leading contribution as $n$ gets large comes from the term with the higest value of $a$ because that term will generally be much bigger than all the others.

 

[micromass]

I'm not sure, that's why I'm asking :(

What does your book or your notes say?