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Math Help - Binomial questions 2

  1. #1
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    Binomial questions 2

    Hi I've some more questions, your help is greatly appreciated!

    1.) (x^2-3x+1)^2=x^4-gx^3+11x^2-6x+1 and the sum of it's coefficients is 1, what is the sum of the coefficients of
    (x^3+2x^2+3x-7)^{100}?

    I really have no idea how to start, can't see any patterns..


    2a.) Prove that r{n \choose r}=n{n-1 \choose r-1}

    I did this ok so ignore this part! I had just typed it down as this part may yield a clue for the other parts.

    2b.) Hence show that {n \choose 1}+2{n \choose 2}+3{n \choose 3}+4{n \choose 4}+...+n{n \choose n}=n2^{n-1}

    2c.) Suppose the numbers Pr ( r is a subscript!) are defined by
    Pr={n \choose r} p^r(1-p)^{n-r} for r=0,1,2,3...,n.

    Prove that

    \sum\limits_{r=0}^nPr=1

    and that

    \sum\limits_{r=1}^nrPr=np

    How do I do them! Please help me thank you so much!!!
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  2. #2
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    Re: Binomial questions 2

    Sorry for question 1, it is not gx^3 but 6x^3, sorry for the typo and thank you!
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