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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.
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A student is allowed to select at most n-blocks from a collection of (2n + 1) books. If the total number of ways in which he can select a book is 63, find the value of n. Solution
cos^2(A)x sin(A)
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