Chapter 4: Q. 43 (page 315)

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$3 \sum_{k = 2}^{25} k^{2} + 2 {\sum k}_{k = 2}^{24} - \sum_{k = 0}^{25} 1$

Short Answer

Expert verified

The expression in one sigma notation is: $1872 + \sum_{k = 2}^{24} (3 k^{2} + 2 k - 1)$

Step by step solution

Step 1. Given information

The expression is:

${3 \sum}_{k = 2}^{25} k^{2} + 2 {\sum k}_{k = 2}^{24} - \sum_{k = 0}^{25} 1$

Step 2. Write expression into one sigma notation:

${3 \sum}_{k = 2}^{25} k^{2} + 2 {\sum k}_{k = 2}^{24} - \sum_{k = 0}^{25} 1 = (\sum_{k = 2}^{24} 3 k^{2} + 3 {(25)}^{2}) + 2 {\sum k}_{k = 2}^{24} - (1 + 1 + \sum_{k = 2}^{24} 1 + 1) = (\sum_{k = 2}^{24} 3 k^{2} + 1875) + {\sum 2 k}_{k = 2}^{24} - (3 + \sum_{k = 2}^{24} 1) = 1875 - 3 + \sum_{k = 2}^{24} (3 k^{2} + 2 k - 1) = 1872 + \sum_{k = 2}^{24} (3 k^{2} + 2 k - 1)$

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Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$3 \sum_{k = 2}^{25} k^{2} + 2 {\sum k}_{k = 2}^{24} - \sum_{k = 0}^{25} 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write expression into one sigma notation:

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Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).3∑k=225k2+2∑kk=224-∑k=0251

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write expression into one sigma notation:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Discrete Mathematics

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
$3 \sum_{k = 2}^{25} k^{2} + 2 {\sum k}_{k = 2}^{24} - \sum_{k = 0}^{25} 1$