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Thên, Sk + 1 = Sk + ak + 1 = (1² + 2² + 32 + 42 + … + k²) + ak + 1· ... ak +1 = (k+1)²2 Use the equation for ak + 1 and Sk to find the equation for Sk + 1. Sk + 1 fill in thisbox please %3D

Thên, Sk + 1 = Sk + ak + 1 = (1² + 2² + 32 + 42 + … + k²) + ak + 1· ... ak +1 = (k+1)²2 Use the equation for ak + 1 and Sk to find the equation for Sk + 1. Sk + 1 fill in thisbox please %3D

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.4: Mathematical Induction
Problem 2ECP
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8.4 q 3 Please answer this question and box the answer that goes in the blank box,thank you. Appreciate it!

Use mathematical induction to prove the formula for all integers n > 1. 12 + 22 + 32 + 42 + ·.. + n2 n(n + 1)(2n + 1) 6. Find S1 when n 1. %3D S1 1 Assume that Sk = 12 + 22 + 32 + 42 + ... + k² = k(k + 1)(2k + 1) Then, Sk + 1 = Sk + ak + 1 = (12 + 22 + 32 + 42 + ... + k) + ak + 1· ak + 1 = (k+1)² Use the equation for ak + 1 and Sk to find the equation for Sk + 1. Sk + 1 fill in this box please. Is this formula valid for all positive integer values of n? Yes O No
Transcribed Image Text:Use mathematical induction to prove the formula for all integers n > 1. 12 + 22 + 32 + 42 + ·.. + n2 n(n + 1)(2n + 1) 6. Find S1 when n 1. %3D S1 1 Assume that Sk = 12 + 22 + 32 + 42 + ... + k² = k(k + 1)(2k + 1) Then, Sk + 1 = Sk + ak + 1 = (12 + 22 + 32 + 42 + ... + k) + ak + 1· ak + 1 = (k+1)² Use the equation for ak + 1 and Sk to find the equation for Sk + 1. Sk + 1 fill in this box please. Is this formula valid for all positive integer values of n? Yes O No
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