Q. 27 Evaluate the sums in Exercises 2... [FREE SOLUTION]

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Chapter 13: Q. 27 (page 1004)

Evaluate the sums in Exercises $23 鈥� 28$ .
${鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3}$

Short Answer

Expert verified

The value of summation is $1260$

Step by step solution

Step 1. Given information

An expression is given as ${鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3}$

Step 2. Evaluating summation

Separate out the terms as and simplify,

${鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3} = {鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} ({鈭�}_{k = 1}^{2} i j^{2} k^{3}) {鈭�}_{k = 1}^{2} i j^{2} k^{3} = i j^{2} 1^{3} + i j^{2} 2^{3} = i j^{2} (1^{3} + 2^{3}) = i j^{2} (1 + 8) = 9 i j^{2}$

Now solve every term similarly,

${鈭�}_{j = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3} = {鈭�}_{j = 1}^{4} {鈭�}_{j = 1}^{3} ({鈭�}_{i = 1}^{2} j^{2} k^{3}) = {鈭�}_{i = 1}^{4} ({鈭�}_{j = 1}^{3} 9 i j^{2}) {鈭�}_{j = 1}^{3} 9 i j^{2} = 9 i ({鈭�}_{j = 1}^{3} j^{2}) = 9 i (1^{2} + 2^{2} + 3^{2}) = 9 i (1 + 4 + 9) = 9 i 脳 14 = 126 i {鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3} = {鈭�}_{i = 1}^{4} ({鈭�}_{j = 1}^{3} 9 i j^{2}) = {鈭�}_{i = 1}^{4} (126 i) = 126 脳 ({鈭�}_{i = 1}^{4} (i)) = 126 脳 (1 + 2 + 3 + 4) = 126 脳 10 = 1260$

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91影视

Evaluate the sums in Exercises $23 鈥� 28$ .
${鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating summation

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91影视

Evaluate the sums in Exercises 23鈥�28.鈭�i=14鈭�j=13鈭�k=12ij2k3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating summation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Statistics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Evaluate the sums in Exercises $23 鈥� 28$ .
${鈭�}_{i = 1}^{4} {鈭�}_{j = 1}^{3} {鈭�}_{k = 1}^{2} i j^{2} k^{3}$