Deriving Nth Power of (a+b): Geometrical Methods

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Homework Help Overview

The discussion revolves around deriving the nth power of the expression (a+b) using various methods, particularly focusing on geometrical approaches. The original poster expresses interest in methods beyond traditional multiplication, the binomial theorem, and Pascal's triangle, specifically mentioning a potential connection to the Pythagorean theorem.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the possibility of alternative methods for deriving (a+b)^n, questioning whether proofs or different expressions are being sought. Some suggest that the original poster may be looking for proofs of the binomial theorem rather than distinct derivation methods.

Discussion Status

The discussion is ongoing, with participants sharing their interpretations of the original poster's request. There is a recognition of the need for clarification on whether proofs or alternative methods are desired, but no consensus has been reached regarding the specific geometrical methods mentioned.

Contextual Notes

The original poster's inquiry is framed within the context of a holiday homework project, which may impose certain constraints on the types of methods considered acceptable for their assignment.

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can u tell me all possible ways of deriving nth power of (a+b) other than -- multiplying (a+b) again and again;binomial theorem and pascal triangle. CAN U TELL ME A FEW MORE METHODS? I'M PARTICULARLY INTERESTED IN GEOMETRICAL METHODS (someone told me there's one using PYTHAGORAS THEOREM). u may think I'm asking u a crazy question , but this is my holiday homework project for maths
 
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The binomial theorem is:

[tex](a+b)^n = \sum_{k=0}^n \left( \begin{array}{cc} n \\ k \end{array} \right)a^k b^{n-k}[/tex]

Are you looking for different ways to prove this? Or different expressions equal to the LHS? Or ways of numerically computing the LHS for specific values of a and b?
 
StatusX said:
The binomial theorem is:

[tex](a+b)^n = \sum_{k=0}^n \left( \begin{array}{cc} n \\ k \end{array} \right)a^k b^{n-k}[/tex]

Are you looking for different ways to prove this? Or different expressions equal to the LHS? Or ways of numerically computing the LHS for specific values of a and b?

Looks GOOD to me =) :-p
 
I think the OP is looking for a proof of the theorem. The obvious ones are the inductive proof and some kind of combinatoric proof (I can think of one, and I imagine others of this kind are essentially the same). I can't, however, imagine a proof based on Pythgoras.
 
No, I don't think so. It seems clear that the OP is looking for different methods of finding (x+ y)n, or at least the coefficients, not just a proof of the binomial theorem. Unfortunately, I can't think of any!
 

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