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Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29+ + (10n-1) = n(5n+4) = ... What is the next step in this induction proof? A. Determine whether the statement holds for any number k +1. B. Assume the statement holds for some k, and determine whether it then holds for k +1. OC. Determine whether the statement holds for some k. If so, it also holds for k +1. O D. Assume that the statement holds for k=1, and determine whether it holds for k = 2.

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29+ + (10n-1) = n(5n+4) = ... What is the next step in this induction proof? A. Determine whether the statement holds for any number k +1. B. Assume the statement holds for some k, and determine whether it then holds for k +1. OC. Determine whether the statement holds for some k. If so, it also holds for k +1. O D. Assume that the statement holds for k=1, and determine whether it holds for k = 2.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29++ (10n-1) = n(5n+4) What is the next step in this induction proof? OA. Determine whether the statement holds for any number k +1. OB. Assume the statement holds for some k, and determine whether it then holds for k +1. OC. Determine whether the statement holds for some k. If so, it also holds for k + 1. OD. Assume that the statement holds for k=1, and determine whether it holds for k = 2. Write the given statement for k +1. 9+19+29++ (10k-1)+=
Transcribed Image Text:Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29++ (10n-1) = n(5n+4) What is the next step in this induction proof? OA. Determine whether the statement holds for any number k +1. OB. Assume the statement holds for some k, and determine whether it then holds for k +1. OC. Determine whether the statement holds for some k. If so, it also holds for k + 1. OD. Assume that the statement holds for k=1, and determine whether it holds for k = 2. Write the given statement for k +1. 9+19+29++ (10k-1)+=
Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29++ (10n-1) = n(5n+ 4) 2 To prove that 9+19+29++ (10n-1) = n(5n+ 4) is true for all natural numbers n, first show that this statement is true for n= Simplify each side of the statement for the appropriate value of n. 9+19+29++ (10n-1) = n(5n+4) What is the next step in this induction proof? O A. Determine whether the statement holds for any number k + 1. OB. Assume the statement holds for some k, and determine whether it then holds for k + 1. OC. Determine whether the statement holds for some k. If so, it also holds for k + 1.
Transcribed Image Text:Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n. 9+19+29++ (10n-1) = n(5n+ 4) 2 To prove that 9+19+29++ (10n-1) = n(5n+ 4) is true for all natural numbers n, first show that this statement is true for n= Simplify each side of the statement for the appropriate value of n. 9+19+29++ (10n-1) = n(5n+4) What is the next step in this induction proof? O A. Determine whether the statement holds for any number k + 1. OB. Assume the statement holds for some k, and determine whether it then holds for k + 1. OC. Determine whether the statement holds for some k. If so, it also holds for k + 1.
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