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Math Help - Pascals triangle...?

  1. #1
    Newbie
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    May 2008
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    Pascals triangle...?

    hey, this is my problem:

    Expand (a+b)^0, (a+b)^1, (a+b)^2, etc

    (a+b)^0 = 1
    (a+b)^1 = a + b
    (a+b)^2 = a^2 + 2ab + b^2
    (a+b)^3 = a^3 + 3a^(2)b + 3a(b^2) + b^3
    (a+b)^4 = a^4 + 4(a^3)b + 6(a^2)(b^2) + b^4

    I can see how this relates to pascals triangle, im just having a bit of trouble with a couple of questions about this...

    What is the sum of the powers in each term of (a+b)^n?

    all i can really think of is (a+b)^n = a^n + a^(n-1)... but im not sure what comes after this.

    honestly i have no idea, but i think its something like that ^

    Or i could be completely wrong. anyway, any help would be appreciated! thanks.
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    802
    Hi

    Let's do it for n=2 : (a+b)^2=a^2+2ab+b^2
    • first term : a^2=a^2b^0 : the sum of the powers is 2+0=2
    • second term : 2ab=2a^1b^1 : the sum of the powers is 1+1=2
    • third term : same idea as in the case of the first one. The result is 2.
    Hope that helps.
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  3. #3
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    yes, that was helpful. thanks
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