Chapter 13: Q. 3 (page 1054)

Explain why ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ .

Short Answer

Expert verified

The two summations ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ contains the same summands although the summands are rearranged by the cumulative and associative properties of addition, they are equal.

Step by step solution

Step 1. Given information

We need to explain why ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ .

Step 2. Definition for the summation:

The summation definition states that if the order of the summation will change but there is no effect on the result. The two summations ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ contains the same summands although the summands are rearranged by the cumulative and associative properties of addition, they are equal.

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Explain why ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Definition for the summation:

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Explain why鈭�i=1l鈭�j=1m鈭�k=1nij2k3=鈭�j=1m鈭�k=1n鈭�i=1lij2k3.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Definition for the summation:

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Statistics

Calculus

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Explain why ${鈭�}_{i = 1}^{l} {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} i j^{2} k^{3} = {鈭�}_{j = 1}^{m} {鈭�}_{k = 1}^{n} {鈭�}_{i = 1}^{l} i j^{2} k^{3}$ .