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(b) Let's rearrange the alternating harmonic series: i. We have = In 2. %3D 3 4. 10 Now group together the terms as follows: 3 10 12 We can write this as a series D' Determine A,B, C, and D. (Think about even and odd numbers.) ii. Explain why this is a rearrangement of the alternating harmonic series. In other words, show that every term from the alternating harmonic series appears somewhere in this new 4- (β-#) & rearrangement. iii. Now do the subtraction that you have in the parenthesis (-) and factor out . Explain how this shows that In 2. .... 3 10 12

(b) Let's rearrange the alternating harmonic series: i. We have = In 2. %3D 3 4. 10 Now group together the terms as follows: 3 10 12 We can write this as a series D' Determine A,B, C, and D. (Think about even and odd numbers.) ii. Explain why this is a rearrangement of the alternating harmonic series. In other words, show that every term from the alternating harmonic series appears somewhere in this new 4- (β-#) & rearrangement. iii. Now do the subtraction that you have in the parenthesis (-) and factor out . Explain how this shows that In 2. .... 3 10 12

Advanced Engineering Mathematics
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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(b) Let's rearrange the alternating harmonic series: i. We have = In 2. %3D 3 4. 10 Now group together the terms as follows: 3 10 12 We can write this as a series D' Determine A,B, C, and D. (Think about even and odd numbers.) ii. Explain why this is a rearrangement of the alternating harmonic series. In other words, show that every term from the alternating harmonic series appears somewhere in this new 4- (β-#) & rearrangement. iii. Now do the subtraction that you have in the parenthesis (-) and factor out . Explain how this shows that In 2. .... 3 10 12
Transcribed Image Text:(b) Let's rearrange the alternating harmonic series: i. We have = In 2. %3D 3 4. 10 Now group together the terms as follows: 3 10 12 We can write this as a series D' Determine A,B, C, and D. (Think about even and odd numbers.) ii. Explain why this is a rearrangement of the alternating harmonic series. In other words, show that every term from the alternating harmonic series appears somewhere in this new 4- (β-#) & rearrangement. iii. Now do the subtraction that you have in the parenthesis (-) and factor out . Explain how this shows that In 2. .... 3 10 12
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