Pascal Triangle: The Negative Side

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Discussion Overview

The discussion revolves around the application of Pascal's Triangle in the context of negative exponents and the implications of extending its use in this manner. Participants explore whether the triangle can be adapted to work with negative values and what that means for its universality.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant proposes the idea of using Pascal's Triangle in an upward direction, suggesting that the opposite side could be represented with a pole at -1, questioning the triangle's universality in a "negative world."
  • Another participant interprets this as an attempt to extend Pascal's Triangle to coefficients of negative exponents, indicating that it can still be utilized by expressing negative exponents as the reciprocal of positive ones.
  • A third participant provides a technical correction regarding the notation for negative exponents in LaTeX, suggesting the proper format for clarity.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Pascal's Triangle to negative exponents, with some suggesting it can be adapted while others question its universality in that context. The discussion remains unresolved regarding the implications of these adaptations.

Contextual Notes

There are limitations in the assumptions made about the applicability of Pascal's Triangle to negative values, and the discussion does not fully resolve the mathematical steps involved in this extension.

krateesh
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Can we use pascal triangle by moving upwards i.e in opposite direction,considering that the opposite side will have their pole as -1?
Mens both 1 & -1 will lie in between the centre.
And what if we remain unipolar with centre as 1?
Surely if both of them fail to give us the required results than we can say that pascal triangle is not universal as it doesn't fair well in negative world.
 
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Basically you wish to extend Pascals Triangle to correspond to the coefficients of negative exponents? i.e [tex](a+b)^[-n][/tex]. But if you recognize, this can also be expressed as [tex]((a+b)^n)^[-1][/tex], or the reciprocal of the absolute value of your negative n. So we can still use the triangle.

Edit: Uhh this tex I am trying to use isn't going too smoothly..the weird stuff ups are ment to be exponents...
 
Last edited:
Use braces for LaTeX:
[tex](a+b)^{-n}[/tex]
[tex]((a+b)^n)^{-1}[/tex]
 
o ok thanks that's what i meant
 

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