A sequence {a^n} of real numbers is defined recursively by a_1=2 for n ≥ 2, a_n=(2+1∙a_1^2+2∙a_2^2+⋯+(n-1) a_(n-1)^2)/n Determine a_(2,) a_3, and a_4. Show all work. Clearly, a_n is a rational number for each n ϵ N. Based on the information in a), however, what conjecture does this suggest?

A sequence {a^n} of real numbers is defined recursively by a_1=2 for n ≥ 2, a_n=(2+1∙a_1^2+2∙a_2^2+⋯+(n-1) a_(n-1)^2)/n Determine a_(2,) a_3, and a_4. Show all work. Clearly, a_n is a rational number for each n ϵ N. Based on the information in a), however, what conjecture does this suggest?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 8RE

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