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Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n-4)=(5n - 3). Find S₁ when n = 1. S₁ = Assume that Sk = 1 + 6 + 11 + 16 + ... + (5k − 4) = ½ (5k − 3). Then, Sk+ 1 = Sk+ªk+ 1 = (1 + 6 + 11 + 16 + ... + ak+1= Use the equation for ak + 1 Sk+1= (5k − 4)) + ªk + 1* and S to find the equation for Sk + 1* k Is this formula valid for all positive integer values of n? Yes No

Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n-4)=(5n - 3). Find S₁ when n = 1. S₁ = Assume that Sk = 1 + 6 + 11 + 16 + ... + (5k − 4) = ½ (5k − 3). Then, Sk+ 1 = Sk+ªk+ 1 = (1 + 6 + 11 + 16 + ... + ak+1= Use the equation for ak + 1 Sk+1= (5k − 4)) + ªk + 1* and S to find the equation for Sk + 1* k Is this formula valid for all positive integer values of n? Yes No

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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Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n = 4) = (5n - (5n - 3). 2 Find S₁ when n = 1. S₁ = Assume that k = 1 + 6 + 11 + 16 + ··· + (5k – 4) = + (5k - 4) =(5k - 3). 2 Sk Then, Sk+1 = Sk+ªk+1 = (1 + 6 + 11 + 16 + TELE .. ak+1= + (5k − 4)) + ªk+1° Use the equation for ak + 1 and S to find the equation for Sk+ k 1ª Sk+1= Is this formula valid for all positive integer values of n? O Yes O No
Transcribed Image Text:Use mathematical induction to prove the formula for all integers n ≥ 1. 1 + 6 + 11 + 16 + ... + (5n = 4) = (5n - (5n - 3). 2 Find S₁ when n = 1. S₁ = Assume that k = 1 + 6 + 11 + 16 + ··· + (5k – 4) = + (5k - 4) =(5k - 3). 2 Sk Then, Sk+1 = Sk+ªk+1 = (1 + 6 + 11 + 16 + TELE .. ak+1= + (5k − 4)) + ªk+1° Use the equation for ak + 1 and S to find the equation for Sk+ k 1ª Sk+1= Is this formula valid for all positive integer values of n? O Yes O No
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