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

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Homework Help Overview

The discussion revolves around verifying the expression (n^2 + 3n - 3)/n^3 in the context of Big O notation, specifically whether it equals 0 + O(2/n). The subject area is primarily focused on asymptotic analysis and the properties of Big O notation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of Big O notation and its implications for convergence rates. Questions arise regarding the interpretation of terms and the significance of leading contributions in the context of asymptotic behavior.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the definitions and implications of Big O notation. Some guidance has been offered regarding the leading contributions to convergence rates, but no consensus or resolution has been reached.

Contextual Notes

There appears to be a lack of specific examples or definitions from textbooks or notes that could aid in understanding the concept of convergence in relation to Big O notation.

JazzRun
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Homework Statement


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


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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.
 
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What does the big O notation mean?
 
a_n converges to A with a rate of convergence O(b_n). Then you can write a_n=A + O(b_n)
 
JazzRun said:
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.
 
I'm not sure, that's why I'm asking :(
 
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.
 
JazzRun said:
I'm not sure, that's why I'm asking :(

What does your book or your notes say?
 

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