For k ≥0, let S be the set of sequences of k non-negative integers, all of which are not equal to 1. For n≥1, let ank denote the number of sequences in S whose sum is n. (a) Write out the sequences in S of length 3 which sum to 3, and write down 03.3. (b) Prove that the generating function s(x) for S is k s(x) = (1-2+2²)* (c) Determine a2k and ask for all k ≥ 1.
For k ≥0, let S be the set of sequences of k non-negative integers, all of which are not equal to 1. For n≥1, let ank denote the number of sequences in S whose sum is n. (a) Write out the sequences in S of length 3 which sum to 3, and write down 03.3. (b) Prove that the generating function s(x) for S is k s(x) = (1-2+2²)* (c) Determine a2k and ask for all k ≥ 1.
Principles Of Marketing
17th Edition
ISBN:9780134492513
Author:Kotler, Philip, Armstrong, Gary (gary M.)
Publisher:Kotler, Philip, Armstrong, Gary (gary M.)
Chapter1: Marketing: Creating Customer Value And Engagement
Section: Chapter Questions
Problem 1.1DQ
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![For k ≥0, let S be the set of sequences of k non-negative integers, all of which are not equal to 1. For
n≥1, let ank denote the number of sequences in S whose sum is n.
(a) Write out the sequences in S of length 3 which sum to 3, and write down 03.3.
(b) Prove that the generating function s(x) for S is
k
s(x) = (1-2+2²)*
(c) Determine a2k and ask for all k ≥ 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a7ad357-00a1-4695-8e06-09f7f8a0441b%2Fe344bd70-4e02-4b91-aaf6-07937ab8d5d5%2Fu27rk8d_processed.png&w=3840&q=75)
Transcribed Image Text:For k ≥0, let S be the set of sequences of k non-negative integers, all of which are not equal to 1. For
n≥1, let ank denote the number of sequences in S whose sum is n.
(a) Write out the sequences in S of length 3 which sum to 3, and write down 03.3.
(b) Prove that the generating function s(x) for S is
k
s(x) = (1-2+2²)*
(c) Determine a2k and ask for all k ≥ 1.
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