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Math Help - last generating function question.

  1. #1
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    last generating function question.

    Im confused by generating functions. Theres the 5 main "rules" that u need to manipulate the expressions given to determine the sequence.

    (4x-1)^3 at first glance i think to use the binomial but the form of it is (1+x)^n = nC0 + nC1 x + nC2 x^2 + ...

    but my issue is i assume that i cant just ignore that they arent of the same form.. but then im lost.
    If anyone can explain it to me id be grateful I really want to actually understand.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by stumped765 View Post
    Im confused by generating functions. Theres the 5 main "rules" that u need to manipulate the expressions given to determine the sequence.

    (4x-1)^3 at first glance i think to use the binomial but the form of it is (1+x)^n = nC0 + nC1 x + nC2 x^2 + ...

    but my issue is i assume that i cant just ignore that they arent of the same form.. but then im lost.
    If anyone can explain it to me id be grateful I really want to actually understand.
    \left(4x-1\right)^3=-\left(1-4x\right)^3=-\left(1+\left(-4x\right)\right)^3. If you let z=-4x this becomes what you desire.
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