Chapter 12: Q. 1TF (page 987)

A Double Summation: Let ${鈭�}_{i = 1}^{m} {鈭�}_{j = 1}^{n} f (i, j) = {鈭�}_{i = 1}^{m} ({鈭�}_{j = 1}^{n} f (i, j))$
Evaluate: ${鈭�}_{i = 1}^{15} {鈭�}_{j = 1}^{10} i j^{2} .$

Short Answer

Expert verified

The value of ${鈭�}_{i = 1}^{15} {鈭�}_{j = 1}^{10} i j^{2}$ is 46,200.

Step by step solution

Step 1. Given Information.

Given: ${鈭�}_{i = 1}^{m} {鈭�}_{j = 1}^{n} f (i, j) = {鈭�}_{i = 1}^{m} ({鈭�}_{j = 1}^{n} f (i, j))$ .

Step 2. Evaluation of the function.

${鈭�}_{i = 1}^{15} {鈭�}_{j = 1}^{10} i j^{2} = {鈭�}_{i = 1}^{15} ({鈭�}_{j = 1}^{10} i j^{2}) = {鈭�}_{i = 1}^{15} (i {鈭�}_{j = 1}^{10} j^{2}) = {鈭�}_{i = 1}^{15} (i (1^{2} + 2^{2} + . . . + 10^{2})) = {鈭�}_{i = 1}^{15} (i (\frac{10 (10 + 1) (20 + 1)}{6})) = (\frac{10 (11) (21)}{6}) {鈭�}_{i = 1}^{15} (i) = (5.11.7) (\frac{15.16}{2}) = 46200 .$

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91影视

A Double Summation: Let ${鈭�}_{i = 1}^{m} {鈭�}_{j = 1}^{n} f (i, j) = {鈭�}_{i = 1}^{m} ({鈭�}_{j = 1}^{n} f (i, j))$
Evaluate: ${鈭�}_{i = 1}^{15} {鈭�}_{j = 1}^{10} i j^{2} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation of the function.

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91影视

A Double Summation: Let 鈭�i=1m鈭�j=1nf(i,j)=鈭�i=1m鈭�j=1nf(i,j)Evaluate:鈭�i=115鈭�j=110ij2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Evaluation of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

A Double Summation: Let ${鈭�}_{i = 1}^{m} {鈭�}_{j = 1}^{n} f (i, j) = {鈭�}_{i = 1}^{m} ({鈭�}_{j = 1}^{n} f (i, j))$
Evaluate: ${鈭�}_{i = 1}^{15} {鈭�}_{j = 1}^{10} i j^{2} .$