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Consider the sum (1-1) + (1-1) + (1-1) +0+0+0+0. S 14 (-1+1) + (-1+1)+1+0+0+0=1. Work through the following problems to determine what is happening here. a. Consider the sequence of partial sums (2k-1)=(a₁ + a₂ + a, 44 (1,0,1,0,1,0,....). Determine whether this sequence converges or diverges. Then prove your result. S-1-141-141-141- On one hand, it seems as though S On the other hand, it seems as though This seems contradictory as 0 * 1. b. What does your answer for part b imply in terms of the infinite sum S = Σ2-19)?

Consider the sum (1-1) + (1-1) + (1-1) +0+0+0+0. S 14 (-1+1) + (-1+1)+1+0+0+0=1. Work through the following problems to determine what is happening here. a. Consider the sequence of partial sums (2k-1)=(a₁ + a₂ + a, 44 (1,0,1,0,1,0,....). Determine whether this sequence converges or diverges. Then prove your result. S-1-141-141-141- On one hand, it seems as though S On the other hand, it seems as though This seems contradictory as 0 * 1. b. What does your answer for part b imply in terms of the infinite sum S = Σ2-19)?

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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I need to solve #9 a by using the negation of convergence. 

9. Consider the sum S1-141-141-141- On one hand, it seems as though S= (1-1) + (1-1)+(1-1) +0+0+0+0. On the other hand, it seems as though S=1+ (-1+1)+(-141)+ 14040401. This seems contradictory as 0 / 1, Work through the following problems to determine what is happening here. a. Consider the sequence of partial sums (2k-1) = (a₁ + a₂ + az + + a) (1,0,1,0,1,0,....), Determine whether this sequence converges or diverges. Then prove your result, b. What does your answer for part b imply in terms of the infinite sum S=2-19}? 10. Prove that any integer that is a perfect cube is no more than one integer away from a multiple of 9,
Transcribed Image Text:9. Consider the sum S1-141-141-141- On one hand, it seems as though S= (1-1) + (1-1)+(1-1) +0+0+0+0. On the other hand, it seems as though S=1+ (-1+1)+(-141)+ 14040401. This seems contradictory as 0 / 1, Work through the following problems to determine what is happening here. a. Consider the sequence of partial sums (2k-1) = (a₁ + a₂ + az + + a) (1,0,1,0,1,0,....), Determine whether this sequence converges or diverges. Then prove your result, b. What does your answer for part b imply in terms of the infinite sum S=2-19}? 10. Prove that any integer that is a perfect cube is no more than one integer away from a multiple of 9,
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