Use mathematical induction to prove the formula for all integers n2 1. 2+ 11 + 20 + 29 + … + (9n – 7) = (9n - 5). Find S, when n = 1. Assume that Sk = 2 + 11 + 20 + 29 + … + (9k – 7) = (9k – 5). ... Then, Sk +1 = Sk + ak + 1 = (2 + 11 + 20 + 29 + …* + (9k – 7)) + ak + 1º ak +1=

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 46E: Use generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection...
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Use mathematical induction to prove the formula for all integers n 2 1.
2 + 11 + 20 + 29 + . + (9n – 7) = "(9n – 5).
Find S, when n = 1.
S =
Assume that
Sk = 2 + 11 + 20 + 29 + ** + (9k – 7) =
(9k – 5).
2
Then,
Sk+1 = Sk + ak+1 = (2 + 11 + 20 + 29 + *** + (9k – 7)) + ak +1°
ak + 1 =
Use the equation for ak +1 and S to find the equation for Sk + 1.
Sk-
Is this formula valid for all positive integer values of n?
O Yes
No
Transcribed Image Text:Use mathematical induction to prove the formula for all integers n 2 1. 2 + 11 + 20 + 29 + . + (9n – 7) = "(9n – 5). Find S, when n = 1. S = Assume that Sk = 2 + 11 + 20 + 29 + ** + (9k – 7) = (9k – 5). 2 Then, Sk+1 = Sk + ak+1 = (2 + 11 + 20 + 29 + *** + (9k – 7)) + ak +1° ak + 1 = Use the equation for ak +1 and S to find the equation for Sk + 1. Sk- Is this formula valid for all positive integer values of n? O Yes No
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