Find the sum. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.) - k2 + 5 k = 4
Find the sum. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.) - k2 + 5 k = 4
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Summation Problem
**Problem Statement:**
Find the sum. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.)
\[
\sum_{k = 4}^{8} \frac{1}{k^2 + 5}
\]
**Answer Input:**
[ ]
In this problem, you are required to compute the sum of the given series from \( k = 4 \) to \( k = 8 \). The term inside the summation is \(\frac{1}{k^2 + 5}\). You can use the summation capabilities of a graphing utility to verify your result, ensuring to round your final answer to four decimal places.
### Instructions:
1. Identify each term in the summation series based on the variable \( k \) values ranging from 4 to 8.
2. Compute the value of each term.
3. Sum the computed values.
4. Verify your result using a graphing utility.
5. Enter your final answer, rounded to four decimal places, in the provided input box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f8727e-6fc0-4de4-b4e0-c04b5e908db0%2Fa159db1a-c625-493a-807f-32378d82a2a3%2Fiz0z6ok_processed.png&w=3840&q=75)
Transcribed Image Text:### Summation Problem
**Problem Statement:**
Find the sum. Use the summation capabilities of a graphing utility to verify your result. (Round your answer to four decimal places.)
\[
\sum_{k = 4}^{8} \frac{1}{k^2 + 5}
\]
**Answer Input:**
[ ]
In this problem, you are required to compute the sum of the given series from \( k = 4 \) to \( k = 8 \). The term inside the summation is \(\frac{1}{k^2 + 5}\). You can use the summation capabilities of a graphing utility to verify your result, ensuring to round your final answer to four decimal places.
### Instructions:
1. Identify each term in the summation series based on the variable \( k \) values ranging from 4 to 8.
2. Compute the value of each term.
3. Sum the computed values.
4. Verify your result using a graphing utility.
5. Enter your final answer, rounded to four decimal places, in the provided input box.
![**Exercise: Use sigma notation to write the sum.**
Consider the following sum expressed in expanded form:
\[ \left[ 1 - \left( \frac{1}{5} \right)^2 \right] + \left[ 1 - \left( \frac{2}{5} \right)^2 \right] + \ldots + \left[ 1 - \left( \frac{5}{5} \right)^2 \right] \]
This sum can be written using sigma notation as follows:
\[ \sum_{j=1}^{5} \left[ 1 - \left( \frac{j}{5} \right)^2 \right] \]
A box is presented to enter the sigma notation, and the valid attempt entered the correct formula:
\[ \sum_{j=1}^{5} \left[ 1 - \left( \frac{j}{5} \right)^2 \right] \]
An incorrect attempt entered:
\[ \sum_{i=1}^{5} 2i \]
The correct entry received a checkmark indicating correctness, while the incorrect entered received an "X".
**Explanation:**
- The top part of the image shows the expanded series using individual terms.
- The lower part of the image shows the sigma notation implementation and the evaluation of correctness.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5f8727e-6fc0-4de4-b4e0-c04b5e908db0%2Fa159db1a-c625-493a-807f-32378d82a2a3%2F41b0e3l_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise: Use sigma notation to write the sum.**
Consider the following sum expressed in expanded form:
\[ \left[ 1 - \left( \frac{1}{5} \right)^2 \right] + \left[ 1 - \left( \frac{2}{5} \right)^2 \right] + \ldots + \left[ 1 - \left( \frac{5}{5} \right)^2 \right] \]
This sum can be written using sigma notation as follows:
\[ \sum_{j=1}^{5} \left[ 1 - \left( \frac{j}{5} \right)^2 \right] \]
A box is presented to enter the sigma notation, and the valid attempt entered the correct formula:
\[ \sum_{j=1}^{5} \left[ 1 - \left( \frac{j}{5} \right)^2 \right] \]
An incorrect attempt entered:
\[ \sum_{i=1}^{5} 2i \]
The correct entry received a checkmark indicating correctness, while the incorrect entered received an "X".
**Explanation:**
- The top part of the image shows the expanded series using individual terms.
- The lower part of the image shows the sigma notation implementation and the evaluation of correctness.
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