Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. A. 1+2+3+4+...+1001 ### Arithmetic Series Sums Using Gauss's ApproachGauss's approach to summing arithmetic series involves recognizing patterns in the sequences and applying a formula for efficiency. #### Problem 1.1.A-1Use the approach in Gauss's **Problem** to find the following sums of arithmetic sequences:#### Questions:**a.** $1 + 2 + 3 + 4 + \ldots + 1001$ **b.** $1 + 3 + 5 + 7 + \ldots + 103$ **c.** $8 + 17 + 26 + 35 + \ldots + 890$ **d.** $293 + 290 + 287 + 284 + \ldots + 2$ #### Example Solution:**a. The sum of the sequence is** \[ \boxed{} \]### Instructions:1. Enter your answer in the answer box and then click **Check Answer**.### Assessment:You have **3 parts** remaining to complete.Utilize the concepts of arithmetic sums, identify common differences, first and last terms of the sequences, and apply the formula for the sum of an arithmetic series:\[ S_n = \frac{n}{2} \times (a + l) \]where:- $ S_n $ is the sum of the arithmetic series,- $ n $ is the number of terms,- $ a $ is the first term,- $ l $ is the last term.You are encouraged to solve each part step-by-step and verify your results.Good luck!

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Description: Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. A. 1+2+3+4+...+1001 ### Arithmetic Series Sums Using Gauss's ApproachGauss's approach to summing arithmetic series involves recognizing patterns in the sequences

Consider the series 1+2+3+4+…+1001. For the series 1+2+3+4+…+1001, it is clear that there are 1001…

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Use the approach in Gauss's Problem to find the following sums of arithmetic sequences. A. 1+2+3+4+...+1001

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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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences.

A. 1+2+3+4+...+1001

### Arithmetic Series Sums Using Gauss's Approach

Gauss's approach to summing arithmetic series involves recognizing patterns in the sequences and applying a formula for efficiency.

#### Problem 1.1.A-1
Use the approach in Gauss's **Problem** to find the following sums of arithmetic sequences:

#### Questions:

**a.** $1 + 2 + 3 + 4 + \ldots + 1001$
**b.** $1 + 3 + 5 + 7 + \ldots + 103$
**c.** $8 + 17 + 26 + 35 + \ldots + 890$
**d.** $293 + 290 + 287 + 284 + \ldots + 2$

#### Example Solution:

**a. The sum of the sequence is** \[ \boxed{} \]

### Instructions:
1. Enter your answer in the answer box and then click **Check Answer**.

### Assessment:

You have **3 parts** remaining to complete.

Utilize the concepts of arithmetic sums, identify common differences, first and last terms of the sequences, and apply the formula for the sum of an arithmetic series:

\[ S_n = \frac{n}{2} \times (a + l) \]

where:
- $ S_n $ is the sum of the arithmetic series,
- $ n $ is the number of terms,
- $ a $ is the first term,
- $ l $ is the last term.

You are encouraged to solve each part step-by-step and verify your results.

Good luck!

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