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(a) The generating function G(z) for a sequence gn is given by
G(z) = 1 - 2z/(1 + 3z)3
Give an explicit formula for gn.
(b) For the sequence gn in the previous part consider the sequence hn defined by hn = 2ng0 + 2n-1g1 + · · ·+gn for all n > 0. Give a closed formula for the generating function H(z) of the sequence hn.
(c) Hence find an explicit formula for hn.
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
4.2^2x+1-9.2^x+1=0
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