Polynomial convergence question.

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Homework Help Overview

The discussion revolves around the convergence of the series SUM n_infinity 1/(n^2 - 4n + 4). Participants are exploring the application of the comparison test and the differences between evaluating limits and sums.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand why dividing by the largest n in the denominator is not applicable for the series, contrasting it with the limit evaluation where such division seems valid. Other participants question the differences between limits and sums, particularly regarding the validity of this approach in each context.

Discussion Status

The discussion is ongoing, with participants raising questions about the validity of certain mathematical approaches and exploring the implications of dividing by the largest power of n in different scenarios. There is no explicit consensus yet, but the dialogue is probing deeper into the concepts involved.

Contextual Notes

Participants are navigating the distinction between limits and infinite sums, with some uncertainty about the application of techniques used in one context to the other. The original poster also expresses confusion regarding the notation SUM and its relation to Riemann sums.

rcmango
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Homework Statement



To find convergence, why can't I divided by the largest n in the denominator in this problem: SUM n_infinity 1/(n^2 - 4n + 4) ?

its suggested to use the comparison test.

(I think SUM stands for E Reimann sum correct?)

but in this problem, I can easily find convergence by dividing by large n in the denominator: lim n->infinity 3n^2/(7n^2 + 1)

?

any explanation please. thanks.

Homework Equations





The Attempt at a Solution



its all above. thanks.
 
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Basically, because one is a limit and one is a sum.
 
Okay, so for a limit, its okay to divide by the largest N, but for a sum it is not common?
 
Do you understand why dividing by the largest power of N, in both numerator and denominator helps you find the limit of a sequence? Would that apply to an infinite sum?
 

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