Chapter 4: Q. 15 (page 403)

The algebra of sums: Fill in the blanks to complete the sum rules that follow. You may assume that $a_{k}$ and $b_{k}$ are functions defined for nonnegative integers $k$ and that $c$ is any real number.
$\sum_{k = 1}^{n} (a_{k} + b_{k}) =$ ______

Short Answer

Expert verified

$\sum_{k = 1}^{n} (a_{k} + b_{k}) = \sum_{k = 1}^{n} a_{k} + \sum_{k = 1}^{n} b_{k}$ .

Step by step solution

Step 1. Given information

$\sum_{k = 1}^{n} (a_{k} + b_{k})$ .

Step 2. Write the sigma notation in expanded form.

$\sum_{k = 1}^{n} (a_{k} + b_{k}) = (a_{1} + b_{1}) + (a_{2} + b_{2}) + (a_{3} + b_{3}) + \dots (a_{n - 1} + b_{n - 1}) + (a_{n} + b_{n})$

Now regroup the terms in sum.

role="math" localid="1648822752316" $= (a_{1} + a_{2} + a_{3} + \dots + a_{n - 1} + a_{n}) + (b_{1} + b_{2} + b_{3} + \dots + b_{n - 1} + b_{n})$

Write the terms in sigma notation.

$= \sum_{k = 1}^{n} a_{k} + \sum_{k = 1}^{n} b_{k}$ .

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The algebra of sums: Fill in the blanks to complete the sum rules that follow. You may assume that $a_{k}$ and $b_{k}$ are functions defined for nonnegative integers $k$ and that $c$ is any real number.
$\sum_{k = 1}^{n} (a_{k} + b_{k}) =$ ______

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the sigma notation in expanded form.

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The algebra of sums: Fill in the blanks to complete the sum rules that follow. You may assume that akand bkare functions defined for nonnegative integers kand that cis any real number.∑k=1nak+bk=______

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the sigma notation in expanded form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Mechanics Maths

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

The algebra of sums: Fill in the blanks to complete the sum rules that follow. You may assume that $a_{k}$ and $b_{k}$ are functions defined for nonnegative integers $k$ and that $c$ is any real number.
$\sum_{k = 1}^{n} (a_{k} + b_{k}) =$ ______