This hypothesis is right about operators on convergent and divergent series?

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Discussion Overview

The discussion revolves around the correctness of a hypothesis related to operators on convergent and divergent series. Participants are examining the implications of applying certain operations to these series and the conditions under which such operations are valid.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the correctness of the hypothesis and seeks clarification on the operations allowed on convergent and divergent series.
  • Multiple participants assert that the hypothesis is incorrect, emphasizing the need to understand convergence issues when dealing with series.
  • Concerns are raised about an error related to treating a convergent series as real numbers rather than considering the implications of divergence.

Areas of Agreement / Disagreement

Participants generally disagree on the correctness of the hypothesis, with multiple viewpoints asserting that it is incorrect due to misunderstandings about convergence.

Contextual Notes

Participants highlight the importance of recognizing the distinction between convergent and divergent series and the potential errors that arise from assuming convergence without justification.

MAGNIBORO
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Sorry for the bad English , do not speak the language very well.
I posted this to know if the statement or " hypothesis " is correct .

thank you very much =D.

First Image:https://gyazo.com/7248311481c1273491db7d3608a5c48e
Second Image:https://gyazo.com/d8fc52d0c99e0094a6a6fa7d0e5273b6
Third Image:https://gyazo.com/035813f059d3eb7bb4131af7cd8f29c3
 
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No, it isn't correct. Learn about convergent and divergent series, and which operations are allowed on them. You need to be very careful with convergence issues.
 
micromass said:
No, it isn't correct. Learn about convergent and divergent series, and which operations are allowed on them. You need to be very careful with convergence issues.
the error is on the part of the two match series with a formula? ( image 2 )
 
MAGNIBORO said:
the error is on the part of the two match series with a formula? ( image 2 )

The error is assuming the series converges and thus can be treated as real numbers instead of infinity.
 
micromass said:
The error is assuming the series converges and thus can be treated as real numbers instead of infinity.
thanks
 

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