Part 2: Applying the Formula for the Sum of the First n integers as shown in 5.2. Make up an original problem similar to example 5.2.2 Evaluate a. Evaluate 2+ 4 + 6 + ... + 200. b. Evaluate 1+ 2 + 3+4+ ... + 300. c. 5+7+9+11+...+159. b. Evaluate 1+ 2 + 3+4+ ... + 300. c.
Part 2: Applying the Formula for the Sum of the First n integers as shown in 5.2. Make up an original problem similar to example 5.2.2 Evaluate a. Evaluate 2+ 4 + 6 + ... + 200. b. Evaluate 1+ 2 + 3+4+ ... + 300. c. 5+7+9+11+...+159. b. Evaluate 1+ 2 + 3+4+ ... + 300. c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Part 2: Applying the Formula for the Sum of the First n integers as shown in 5.2. Make up an original problem similar to example 5.2.2
Evaluate
a. Evaluate 2+ 4 + 6 + ... + 200.
b. Evaluate 1+ 2 + 3+4+ ... + 300.
c. 5+7+9+11+...+159.
b. Evaluate 1+ 2 + 3+4+ ... + 300.
c.
![### Theorem 5.2.1: Sum of the First n Integers
For every integer \( n \geq 1 \),
\[ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. \]
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### Definition
If a sum with a variable number of terms is shown to equal an expression that does not contain either an ellipsis or a summation symbol, we say that the sum is written in **closed form**.
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This content explains a fundamental theorem and associated definition in mathematics, particularly on the topic of summing the first \( n \) integers. The theorem provides a formula to find the sum of the first \( n \) natural numbers efficiently, which is represented in a closed form as \( \frac{n(n+1)}{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2b4e390-596f-48e2-849d-32f83635f844%2F0f1f0c5b-10f0-4a97-91ad-aed60c47d1b0%2Fwz2n8d7.png&w=3840&q=75)
Transcribed Image Text:### Theorem 5.2.1: Sum of the First n Integers
For every integer \( n \geq 1 \),
\[ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. \]
---
### Definition
If a sum with a variable number of terms is shown to equal an expression that does not contain either an ellipsis or a summation symbol, we say that the sum is written in **closed form**.
---
This content explains a fundamental theorem and associated definition in mathematics, particularly on the topic of summing the first \( n \) integers. The theorem provides a formula to find the sum of the first \( n \) natural numbers efficiently, which is represented in a closed form as \( \frac{n(n+1)}{2} \).
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