Use the substitution method, find the closed-form formula of S5(n) = 15 + 25 + · · · + n5 . [You need to describe the process that you guess the formula of S5(n). You also need to include a rigorous induction proof. ]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
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Use the substitution method, find the closed-form formula of

S5(n) = 15 + 25 + · · · + n5 .

[You need to describe the process that you guess the formula of S5(n). You also need to include a rigorous induction proof. ]

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