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)
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)+=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe88ba205-1ef5-4c9b-bc8a-d6f3eacaf2aa%2Fade954b5-b383-4829-bdc5-4205573ea882%2Fuk4o2i_processed.jpeg&w=3840&q=75)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe88ba205-1ef5-4c9b-bc8a-d6f3eacaf2aa%2Fade954b5-b383-4829-bdc5-4205573ea882%2Fnkn5zeu_processed.jpeg&w=3840&q=75)
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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