3. (a) Find a closed formula for the generating function A(z) of the sequence an (3n-7) (-2)".

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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3.
(a) Find a closed formula for the generating function A(z) of the sequence
an = (3n - 7) (-2)".
(b) Find a closed formula for the generating function of the sequence
Sn = ao + a₁ ++ an, where an is defined in part (a).
(c) Use your answer to part (b) or otherwise, to calculate the sum
ao + a₁ ++ an, where an is defined in part (a).
(d)
Write the generating function B(z) of the sequence
bn = (n + 1) 3 ao+n3n-¹a₁ +...+ an
in terms of A(z) (you do not need to use any explicit form of A(z)).
Transcribed Image Text:3. (a) Find a closed formula for the generating function A(z) of the sequence an = (3n - 7) (-2)". (b) Find a closed formula for the generating function of the sequence Sn = ao + a₁ ++ an, where an is defined in part (a). (c) Use your answer to part (b) or otherwise, to calculate the sum ao + a₁ ++ an, where an is defined in part (a). (d) Write the generating function B(z) of the sequence bn = (n + 1) 3 ao+n3n-¹a₁ +...+ an in terms of A(z) (you do not need to use any explicit form of A(z)).
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