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Prove the following statement. a-b is a factor of a - b [ Hint: ak+1-bk +1 = a(ak-bk) + bk (a−b)]. FEED OA. No, because it can be shown that a-b is not always a factor of ak+1-bk+1 even when a - b is a factor of a - bk. OB. No, because it cannot be assumed that a-b is a factor of a - b OC. Yes, because since it is assumed that a-b is a factor of ak-bk, it is known that a-b is also a factor for n=k+1 OD. Yes, because it can be shown that a-b must be a factor of a +1 - b if a-b is a factor of a - bk What is the conclusion? Choose the correct conclusion below. A. The statement is not true for n=1. It holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it only holds for the natural number k+1. OB. The statement is true for n=1. It also holds for k +1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it holds for the first k + 1 natural m

Prove the following statement. a-b is a factor of a - b [ Hint: ak+1-bk +1 = a(ak-bk) + bk (a−b)]. FEED OA. No, because it can be shown that a-b is not always a factor of ak+1-bk+1 even when a - b is a factor of a - bk. OB. No, because it cannot be assumed that a-b is a factor of a - b OC. Yes, because since it is assumed that a-b is a factor of ak-bk, it is known that a-b is also a factor for n=k+1 OD. Yes, because it can be shown that a-b must be a factor of a +1 - b if a-b is a factor of a - bk What is the conclusion? Choose the correct conclusion below. A. The statement is not true for n=1. It holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it only holds for the natural number k+1. OB. The statement is true for n=1. It also holds for k +1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it holds for the first k + 1 natural m

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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< Prove the following statement. a-b is a factor of an - b [ Hint: ak+1-bk +1 = a(ak - bk) + bk (a−b)]. CHEEER OA. No, because it can be shown that a-b is not always a factor of a +1 - bk+1 even when a - b is a factor of a - b B. No, because it cannot be assumed that a - b is a factor of a - b*. OC. Yes, because since it is assumed that a - b is a factor of a - bk, it is known that a-b is also a factor for n=k+1. k+1 k+1 OD. Yes, because it can be shown that a-b must be a factor of a What is the conclusion? Choose the correct conclusion below. A. The statement is not true for n=1. It holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it only holds for the natural numbers, k k+1. - b if a - b is a factor of a - bk C OB. The statement is true for n=1. It also holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it holds for the first k + 1 natural numb The statement in trin for n-1 It does not hold for I +1 miven that it holde for l Thorofor hus the Drinciple of Mathematical Induction it holde for all natural numhare unt
Transcribed Image Text:< Prove the following statement. a-b is a factor of an - b [ Hint: ak+1-bk +1 = a(ak - bk) + bk (a−b)]. CHEEER OA. No, because it can be shown that a-b is not always a factor of a +1 - bk+1 even when a - b is a factor of a - b B. No, because it cannot be assumed that a - b is a factor of a - b*. OC. Yes, because since it is assumed that a - b is a factor of a - bk, it is known that a-b is also a factor for n=k+1. k+1 k+1 OD. Yes, because it can be shown that a-b must be a factor of a What is the conclusion? Choose the correct conclusion below. A. The statement is not true for n=1. It holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it only holds for the natural numbers, k k+1. - b if a - b is a factor of a - bk C OB. The statement is true for n=1. It also holds for k + 1, given that it holds for k. Therefore, by the Principle of Mathematical Induction, it holds for the first k + 1 natural numb The statement in trin for n-1 It does not hold for I +1 miven that it holde for l Thorofor hus the Drinciple of Mathematical Induction it holde for all natural numhare unt
K Prove the following statement. a-b is a factor of a" - b k+1 Hint: a -bk+1 = a(ak-bk) + bk (a−b)]. Does condition I of the Principle of Mathematical Induction holds true for the given equation? OA. Yes, because if 1 is substituted for n, then the resulting expression is true. OB. Yes, because if k is substituted for n, then the resulting expression is equivalent to the original expression. OC. No, because if k is substituted for n, then the resulting expression is different than the original expression. OD. No, because if 1 is substituted for n, then the resulting expression is false. Now check whether condition II of the Principle of Mathematical Induction holds true. Assume that the statement holds for some natural number k. So, a-b is a factor of a - bk. Does condition II of the Principle of Mathematical Induction hold true for the given equation? OA. No, because it can be shown that a - b is not always a factor of a k+1 V CITR V k+1 even when a - b is a factor of a
Transcribed Image Text:K Prove the following statement. a-b is a factor of a" - b k+1 Hint: a -bk+1 = a(ak-bk) + bk (a−b)]. Does condition I of the Principle of Mathematical Induction holds true for the given equation? OA. Yes, because if 1 is substituted for n, then the resulting expression is true. OB. Yes, because if k is substituted for n, then the resulting expression is equivalent to the original expression. OC. No, because if k is substituted for n, then the resulting expression is different than the original expression. OD. No, because if 1 is substituted for n, then the resulting expression is false. Now check whether condition II of the Principle of Mathematical Induction holds true. Assume that the statement holds for some natural number k. So, a-b is a factor of a - bk. Does condition II of the Principle of Mathematical Induction hold true for the given equation? OA. No, because it can be shown that a - b is not always a factor of a k+1 V CITR V k+1 even when a - b is a factor of a
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