Prove that sin (n^2) + sin (n^3) is not a convergent

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    Convergent Sin
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Discussion Overview

The discussion centers around the convergence of the sequence defined by the expression \(\sin(n^2) + \sin(n^3)\). Participants explore the properties of this sequence and compare it to simpler cases involving \(\sin(n)\) and \(\sin(\pi n)\).

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant requests a proof that \(\sin(n^2) + \sin(n^3)\) is not a convergent sequence.
  • Another participant expresses a negative sentiment towards the task, stating "Unpleasant!"
  • A different participant suggests examining \(\sin(n)\) instead, indicating it is an interesting case compared to \(\sin(\pi n)\).
  • Another participant reiterates the suggestion to focus on \(\sin(n)\), proposing specific values of \(n\) such as 3, 31, 314, 3141, and 31415 as examples.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the convergence of \(\sin(n^2) + \sin(n^3)\), and there are multiple competing views regarding the relevance and interest of different sine functions.

Contextual Notes

The discussion does not provide a formal mathematical framework or definitions for convergence, and the implications of the proposed examples are not fully explored.

Kummer
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Prove that [tex]\sin (n^2) + \sin (n^3)[/tex] is not a convergent sequence.
 
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Unpleasant!
 
how about just sin(n). that's already interesting. as opposed to sin(pi n) for example.
 
mathwonk said:
how about just sin(n).
I believe that is easier. Consider n=3,31,314,3141,31415,...
 

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