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,...
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MAKE SURE THAT YOU SHOW ALL WORK AND FULLY EXPLAIN YOU SOLUTION!!!!!!!!!!
3.
Rewrite the series as a sum (show all work).
![### Summation Notation Explained
In the image above, we see a summation notation which is a mathematical way of expressing the addition of a sequence of numbers. The elements are defined by a specific rule applied to indexes within a given range.
The general summation notation looks like this:
\[
\sum_{i=a}^{b} f(i)
\]
Where:
- \( \Sigma \) is the summation symbol.
- \( i \) is the index of summation.
- \( a \) is the starting value of \( i \).
- \( b \) is the ending value of \( i \).
- \( f(i) \) is the function of \( i \) to be summed.
In the provided summation expression, we have:
\[
\sum_{i=0}^{12} (100 - 2i)
\]
This means we are summing up the values of the function \( 100 - 2i \) for \( i \) ranging from 0 to 12.
Let's break down the calculation:
1. **Start with \( i = 0 \):**
\[ 100 - 2(0) = 100 \]
2. **Next, \( i = 1 \):**
\[ 100 - 2(1) = 98 \]
3. **Next, \( i = 2 \):**
\[ 100 - 2(2) = 96 \]
4. **Continue this process for \( i = 3 \) to \( i = 12 \):**
\[ 100 - 2(3) = 94 \]
\[ 100 - 2(4) = 92 \]
\[ 100 - 2(5) = 90 \]
\[ 100 - 2(6) = 88 \]
\[ 100 - 2(7) = 86 \]
\[ 100 - 2(8) = 84 \]
\[ 100 - 2(9) = 82 \]
\[ 100 - 2(10) = 80 \]
\[ 100 - 2(11) = 78 \]
\[ 100 - 2(12) = 76 \]
Adding all these values together will give us the total sum:
\[
100 + 98 + 96 + 94 + 92 + 90 + 88 + 86 +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeea96f9-d9e2-4e41-9df9-d54882930b66%2Ff9814a9b-b94a-4077-8f30-171182410f84%2F3em6pifk_processed.png&w=3840&q=75)
Transcribed Image Text:### Summation Notation Explained
In the image above, we see a summation notation which is a mathematical way of expressing the addition of a sequence of numbers. The elements are defined by a specific rule applied to indexes within a given range.
The general summation notation looks like this:
\[
\sum_{i=a}^{b} f(i)
\]
Where:
- \( \Sigma \) is the summation symbol.
- \( i \) is the index of summation.
- \( a \) is the starting value of \( i \).
- \( b \) is the ending value of \( i \).
- \( f(i) \) is the function of \( i \) to be summed.
In the provided summation expression, we have:
\[
\sum_{i=0}^{12} (100 - 2i)
\]
This means we are summing up the values of the function \( 100 - 2i \) for \( i \) ranging from 0 to 12.
Let's break down the calculation:
1. **Start with \( i = 0 \):**
\[ 100 - 2(0) = 100 \]
2. **Next, \( i = 1 \):**
\[ 100 - 2(1) = 98 \]
3. **Next, \( i = 2 \):**
\[ 100 - 2(2) = 96 \]
4. **Continue this process for \( i = 3 \) to \( i = 12 \):**
\[ 100 - 2(3) = 94 \]
\[ 100 - 2(4) = 92 \]
\[ 100 - 2(5) = 90 \]
\[ 100 - 2(6) = 88 \]
\[ 100 - 2(7) = 86 \]
\[ 100 - 2(8) = 84 \]
\[ 100 - 2(9) = 82 \]
\[ 100 - 2(10) = 80 \]
\[ 100 - 2(11) = 78 \]
\[ 100 - 2(12) = 76 \]
Adding all these values together will give us the total sum:
\[
100 + 98 + 96 + 94 + 92 + 90 + 88 + 86 +
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