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(a) Show for n = 6 that ao, ..., ag is log-concave. (b) Show for general n that ag, ..., an is log-concave. (Note: log-concave sequences are a subject of modern research in combinatorics.)

(a) Show for n = 6 that ao, ..., ag is log-concave. (b) Show for general n that ag, ..., an is log-concave. (Note: log-concave sequences are a subject of modern research in combinatorics.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 14E
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Let n be a positive integer. A sequence of positive integers ao,..., an is log-concave if a > ak-10k+1 for all 1 <k<n- 1. Define a, = (E) for 0 <k < n.
Transcribed Image Text:Let n be a positive integer. A sequence of positive integers ao,..., an is log-concave if a > ak-10k+1 for all 1 <k<n- 1. Define a, = (E) for 0 <k < n.
(a) Show for n = 6 that ao, ..., a6 is log-concave. (b) Show for general n that ao, ..., an is log-concave. (Note: log-concave sequences are a subject of modern research in combinatorics.)
Transcribed Image Text:(a) Show for n = 6 that ao, ..., a6 is log-concave. (b) Show for general n that ao, ..., an is log-concave. (Note: log-concave sequences are a subject of modern research in combinatorics.)
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