Click and drag the steps in the correct order to show that n². - 1 is divisible by 8 is true whenever n is an odd positive integer using mathematical induction. BASIS STEP: INDUCTIVE STEP: Thus, ((2k + 1)² - 1) should be a multiple of 8. Therefore, 8 divides n²-1 whenever n is an odd positive integer. (2k + 1)²-1((2k-1)² - 1) = 8k is a multiple of 8 and by inductive hypothesis, ((2k + 1)² - 1) is a multiple of 8. We can rewrite the given statement as (2n-1)²- 1 is divisible by 8, whenever n is a positive integer. (2k + 1)²-1-((2k-1)² - 1) = 8k is a multiple of 8, and by inductive hypothesis, ((2k-1)²-1) is a multiple of 8. 81 ((21-1)2-1), i.e., 810 Suppose 8 I ((2k-1)²-1). We should prove that 81 ((2k + 1)² - 1). Suppose that 8 I ((2k-1)²-1). We should prove that 81 ((2(k-1)² + 1).
Click and drag the steps in the correct order to show that n². - 1 is divisible by 8 is true whenever n is an odd positive integer using mathematical induction. BASIS STEP: INDUCTIVE STEP: Thus, ((2k + 1)² - 1) should be a multiple of 8. Therefore, 8 divides n²-1 whenever n is an odd positive integer. (2k + 1)²-1((2k-1)² - 1) = 8k is a multiple of 8 and by inductive hypothesis, ((2k + 1)² - 1) is a multiple of 8. We can rewrite the given statement as (2n-1)²- 1 is divisible by 8, whenever n is a positive integer. (2k + 1)²-1-((2k-1)² - 1) = 8k is a multiple of 8, and by inductive hypothesis, ((2k-1)²-1) is a multiple of 8. 81 ((21-1)2-1), i.e., 810 Suppose 8 I ((2k-1)²-1). We should prove that 81 ((2k + 1)² - 1). Suppose that 8 I ((2k-1)²-1). We should prove that 81 ((2(k-1)² + 1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Click and drag the steps in the correct order to show that n²-1 is divisible by 8 is true whenever n is an odd positive integer using
mathematical induction.
BASIS STEP:
INDUCTIVE STEP:
Thus, ((2k + 1)² - 1) should be a multiple of 8.
Therefore, 8 divides n²-1 whenever n is an odd
positive integer.
(2k + 1)²1-((2k-1)² - 1) = 8k is a multiple of
8 and by inductive hypothesis, ((2k + 1)² - 1) is a
multiple of
We can rewrite the given statement as (2n-1)²-
1 is divisible by 8, whenever n is a positive
integer.
(2k + 1)²-1((2k-1)² - 1) = 8k is a multiple of
8, and by inductive hypothesis, ((2k-1)² – 1) is a
multiple of 8.
81 ((211)²-1), i.e., 810
Suppose 8 I ((2k-1)²-1). We should prove that
81 ((2k + 1)² - 1).
Suppose that 8 | ((2k-1)²-1). We should prove
that 8 | ((2(k-1)² + 1).
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