Limit of an Arithmetic Series: Solving for the Limit as n Approaches Infinity

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Homework Help Overview

The discussion revolves around finding the limit of an arithmetic series as n approaches infinity, specifically focusing on the expression Limn→∞ (n²/(1+5+9+...+(4n-3))).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the formulation of the limit and the summation of the arithmetic series in the denominator. Some express uncertainty about how to approach the problem and seek hints or clues.

Discussion Status

There are varying levels of understanding among participants, with some providing potential answers while others are still seeking guidance. The discussion includes attempts to clarify the series and its implications for the limit.

Contextual Notes

Some participants reference previous suggestions and responses, indicating a progression in the discussion, but there is no consensus on the correctness of the proposed answers.

dannysaf
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Limn→∞ (n2/1+5+9+...+(4n-3))
 
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Since you apparently didn't take VietDao's suggestion, I'll tell you the answer is 1/2 and let you figure out if it's correct or not.
 
I have no idea how to do it...so I am asking to give me a clue to this problem!
 
The denominator is an arithmetic series, which sums to 2n2 - n. Therefore the limit is 1/2.
 

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