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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![### Assignment Detail: Sum Calculation
#### Task Description:
You are required to find the value of the following summation:
\[ \sum_{k=1}^{8} 2(5)^k \]
Please enter your answer in the provided text box and click the "Submit Question" button to submit your response.
#### Instructions:
1. Analyze the summation expression to understand the range and function to be summed.
2. Compute the value of the sum meticulously.
3. Input your answer into the text box accurately.
4. Ensure to click the "Submit Question" button to finalize your submission.
#### Summation Explained:
In this problem, you are asked to compute the sum of a series from \( k = 1 \) to \( k = 8 \). The general term of the series is \( 2(5)^k \). This means for each value of \( k \) from 1 to 8, you need to plug in \( k \) into the function \( 2(5)^k \), and then sum all these values.
Mathematically, it is represented by:
\[ \sum_{k=1}^{8} 2(5)^k = 2(5)^1 + 2(5)^2 + 2(5)^3 + \cdots + 2(5)^8 \]
#### Calculator and Input:
- Use a calculator or appropriate software to determine the sum.
- Enter the obtained result into the text box.
- Upon completion, ensure to submit your answer by clicking the "Submit Question" button.
#### Example Solver Section:
To illustrate the process, let's compute the first few terms:
- For \( k = 1 \), \( 2(5)^1 = 2 \times 5 = 10 \)
- For \( k = 2 \), \( 2(5)^2 = 2 \times 25 = 50 \)
- For \( k = 3 \), \( 2(5)^3 = 2 \times 125 = 250 \)
Continue this process until \( k = 8 \), and then sum all those results together.
Good luck, and don't forget to verify your final answer before submission!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45a38a2f-ec58-4f95-82e3-179142041ecb%2F8eccc5a8-19fa-42de-a7a2-6c0bc60f66cd%2F3766u2.png&w=3840&q=75)
Transcribed Image Text:### Assignment Detail: Sum Calculation
#### Task Description:
You are required to find the value of the following summation:
\[ \sum_{k=1}^{8} 2(5)^k \]
Please enter your answer in the provided text box and click the "Submit Question" button to submit your response.
#### Instructions:
1. Analyze the summation expression to understand the range and function to be summed.
2. Compute the value of the sum meticulously.
3. Input your answer into the text box accurately.
4. Ensure to click the "Submit Question" button to finalize your submission.
#### Summation Explained:
In this problem, you are asked to compute the sum of a series from \( k = 1 \) to \( k = 8 \). The general term of the series is \( 2(5)^k \). This means for each value of \( k \) from 1 to 8, you need to plug in \( k \) into the function \( 2(5)^k \), and then sum all these values.
Mathematically, it is represented by:
\[ \sum_{k=1}^{8} 2(5)^k = 2(5)^1 + 2(5)^2 + 2(5)^3 + \cdots + 2(5)^8 \]
#### Calculator and Input:
- Use a calculator or appropriate software to determine the sum.
- Enter the obtained result into the text box.
- Upon completion, ensure to submit your answer by clicking the "Submit Question" button.
#### Example Solver Section:
To illustrate the process, let's compute the first few terms:
- For \( k = 1 \), \( 2(5)^1 = 2 \times 5 = 10 \)
- For \( k = 2 \), \( 2(5)^2 = 2 \times 25 = 50 \)
- For \( k = 3 \), \( 2(5)^3 = 2 \times 125 = 250 \)
Continue this process until \( k = 8 \), and then sum all those results together.
Good luck, and don't forget to verify your final answer before submission!
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