Sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?

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Homework Help Overview

The discussion revolves around the divergence of the expression sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n), with a focus on rigorous proof techniques suitable for a real analysis class.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the asymptotic equivalence of the expression to 1/2n and its implications for divergence. Questions arise regarding the rigor required for the proof, with suggestions of using the limit comparison test versus the comparison test.

Discussion Status

There is an ongoing exploration of proof methods, with some participants suggesting the limit comparison test as a suitable approach. The discussion reflects differing opinions on the adequacy of various testing methods without reaching a consensus.

Contextual Notes

Participants are considering the requirements of a rigorous proof in the context of a real analysis class, indicating that specific standards may apply to the proof's structure and methodology.

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Homework Statement


How to show that sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?


Homework Equations





The Attempt at a Solution


The above expression is asymptotically equivalent to 1/2n which diverges as the harmonic series diverges.

However, a rigorous proof is required for the real analysis class.
 
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grossgermany said:

Homework Statement


How to show that sqrt(4n)/sqrt(4n-3)sqrt(4n^2-3n) diverges?


Homework Equations





The Attempt at a Solution


The above expression is asymptotically equivalent to 1/2n which diverges as the harmonic series diverges.

However, a rigorous proof is required for the real analysis class.
How rigorous? Would the limit comparison test be rigorous enough?
 
Yes, comparison test would be great.
 
I would use the limit comparison test, not the comparison test. For the comparison test, and some series [itex]\sum b_n[/itex] that is known to diverge, you would have to show that an >= bn for all n >= n0.

For the limit comparison test, you only need to look at lim an/bn.
 

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