Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
![### Sum Calculation Problem
#### Problem Statement:
Compute the sum of the series given by the following expression:
\[
\sum_{x=1}^{100} n
\]
#### Options:
- 101
- 10,100
- 1010
- 5050
In this problem, you are required to calculate the sum of the first 100 natural numbers. Select the correct answer from the given options.
(Note: There are no graphs or diagrams associated with this problem. The equation and options are purely textual.)
---
### Explanation:
To solve this problem, you need to recognize that the sum of the first \( n \) natural numbers can be calculated using the formula:
\[
S = \frac{n(n+1)}{2}
\]
For \( n = 100 \):
\[
S = \frac{100 \times 101}{2} = 5050
\]
So, the correct answer is:
- **5050**
---
Practice more problems to strengthen your understanding of series and summations!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F253ec4e6-fefa-47c2-a875-f6d418ff65f8%2Ff13e2894-bf7c-443b-ba49-280eb93fc62e%2F1493v3g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sum Calculation Problem
#### Problem Statement:
Compute the sum of the series given by the following expression:
\[
\sum_{x=1}^{100} n
\]
#### Options:
- 101
- 10,100
- 1010
- 5050
In this problem, you are required to calculate the sum of the first 100 natural numbers. Select the correct answer from the given options.
(Note: There are no graphs or diagrams associated with this problem. The equation and options are purely textual.)
---
### Explanation:
To solve this problem, you need to recognize that the sum of the first \( n \) natural numbers can be calculated using the formula:
\[
S = \frac{n(n+1)}{2}
\]
For \( n = 100 \):
\[
S = \frac{100 \times 101}{2} = 5050
\]
So, the correct answer is:
- **5050**
---
Practice more problems to strengthen your understanding of series and summations!
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