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Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²). (2³) ΣΗ) Σ Filli i=0 (a) Is this statement always true? If not, give an example of sequences {1₁} and {y} such that the equality does not hold. 304 CHAPTER 10 SIGMA NOTATION (b) Is this statement ever true? If possible, give an example of sequences {z} and {y} such that the equality does hold.

Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²). (2³) ΣΗ) Σ Filli i=0 (a) Is this statement always true? If not, give an example of sequences {1₁} and {y} such that the equality does not hold. 304 CHAPTER 10 SIGMA NOTATION (b) Is this statement ever true? If possible, give an example of sequences {z} and {y} such that the equality does hold.

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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Please do Exercise 10.2.4 part A and B and please show step by step and explain. 

Στ x +Σ=Σ(mi + m) i=0 jul i=0 (10.2.2)
Transcribed Image Text:Στ x +Σ=Σ(mi + m) i=0 jul i=0 (10.2.2)
Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ.). (Σκ) Σ (»). 304 || (a) Is this statement always true? If not, give an example of sequences {r} and {y} such that the equality does not hold. CHAPTER 10 SIGMA NOTATION (b) Is this statement ever true? If possible, give an example of sequences {i} and {y} such that the equality does hold.
Transcribed Image Text:Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ.). (Σκ) Σ (»). 304 || (a) Is this statement always true? If not, give an example of sequences {r} and {y} such that the equality does not hold. CHAPTER 10 SIGMA NOTATION (b) Is this statement ever true? If possible, give an example of sequences {i} and {y} such that the equality does hold.
Expert Solution
Step 1

Given equality:

∑i=0nxi·∑i=0nyi=∑i=0nxiyi

 

a) Verify the equality is always true.

If not, give an example.

b) Verify the equality is ever true.

If possible, give an example.

 

steps

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