Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Rewrite the series as a sum (show all work).
![### Summation in Mathematics
In this section, we illustrate how to perform a summation operation in a sequence.
#### Understanding Summation Notation
The image displays a mathematical summation notation:
\[
\sum_{i=0}^{12} (100 - 2i)
\]
This notation tells us to sum the expression \(100 - 2i\) as \(i\) takes on values from 0 to 12 inclusive.
#### Steps to Compute the Summation
1. **Identify the Expression and Limits**:
- **Expression**: \(100 - 2i\)
- **Lower Limit (i=0)**: The summation starts at \(i=0\)
- **Upper Limit (i=12)**: The summation ends at \(i=12\)
2. **Substitute and Sum**:
- Substitute \(i = 0\) to get \(100 - 2(0) = 100\)
- Substitute \(i = 1\) to get \(100 - 2(1) = 98\)
- Substitute \(i = 2\) to get \(100 - 2(2) = 96\)
- Continue this process until \(i = 12\).
The sequence of terms will be: \(100, 98, 96, 94, \ldots, 76\).
3. **Add the Terms**:
\[
100 + 98 + 96 + 94 + 92 + 90 + 88 + 86 + 84 + 82 + 80 + 78 + 76
\]
By calculating these, you will find the result of the summation.
#### Visualization
If you were to graph these terms, you would plot each term on the y-axis against its corresponding \(i\) value on the x-axis. This would create a straight line, demonstrating a linear decrease in values as \(i\) increases.
This process demonstrates how summation notation is used to succinctly describe the addition of a sequence of numbers, which is a fundamental concept in mathematics.
---
This explanation helps you understand the concept of summation, providing you with both the theoretical background and a step-by-step process to solve the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeea96f9-d9e2-4e41-9df9-d54882930b66%2Fd7cb78ce-b3b0-4741-8bd7-e2621f982f0c%2Fg9tiq5_processed.png&w=3840&q=75)
Transcribed Image Text:### Summation in Mathematics
In this section, we illustrate how to perform a summation operation in a sequence.
#### Understanding Summation Notation
The image displays a mathematical summation notation:
\[
\sum_{i=0}^{12} (100 - 2i)
\]
This notation tells us to sum the expression \(100 - 2i\) as \(i\) takes on values from 0 to 12 inclusive.
#### Steps to Compute the Summation
1. **Identify the Expression and Limits**:
- **Expression**: \(100 - 2i\)
- **Lower Limit (i=0)**: The summation starts at \(i=0\)
- **Upper Limit (i=12)**: The summation ends at \(i=12\)
2. **Substitute and Sum**:
- Substitute \(i = 0\) to get \(100 - 2(0) = 100\)
- Substitute \(i = 1\) to get \(100 - 2(1) = 98\)
- Substitute \(i = 2\) to get \(100 - 2(2) = 96\)
- Continue this process until \(i = 12\).
The sequence of terms will be: \(100, 98, 96, 94, \ldots, 76\).
3. **Add the Terms**:
\[
100 + 98 + 96 + 94 + 92 + 90 + 88 + 86 + 84 + 82 + 80 + 78 + 76
\]
By calculating these, you will find the result of the summation.
#### Visualization
If you were to graph these terms, you would plot each term on the y-axis against its corresponding \(i\) value on the x-axis. This would create a straight line, demonstrating a linear decrease in values as \(i\) increases.
This process demonstrates how summation notation is used to succinctly describe the addition of a sequence of numbers, which is a fundamental concept in mathematics.
---
This explanation helps you understand the concept of summation, providing you with both the theoretical background and a step-by-step process to solve the problem.
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