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Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.

  1. Nov 19, 2012 #1
    Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.



    nCr formula: n!/r!(n-r)!



    I've tried everything I can but I don't know how to approach this question.
     
  2. jcsd
  3. Nov 19, 2012 #2
    Have you tried induction?

    You might try (x + y)^1 show that the coefficients are 1 and 1; and then assume it's true for (x+y)^n and show if that is true then it works for the row (x + y) ^(n+1).

    I haven't tried that; but it would be my first try.
     
  4. Nov 19, 2012 #3

    haruspex

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    I would go with JimRoo's first suggestion, induction. You haven't said what definition you have for the terms in Pascal's triangle. I assume it's summing pairs of adjacent entries in one row to generate the next. Use that.
     
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