Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Find the sum.
37+38+39+40+...103+104
![### Summation Problem
#### Problem Statement:
Find the sum \( 37 + 38 + 39 + 40 + \ldots + 103 + 104 \).
#### Answer Box:
The sum is \[ \_\_\_\_\_\}.
#### Instructions:
Enter your answer in the answer box and then click "Check Answer".
---
#### Explanation:
In this problem, we are asked to find the sum of a sequence of consecutive integers starting from 37 and ending at 104.
To solve this, we can use the formula for the sum of an arithmetic series:
\[ \text{Sum} = \frac{n}{2} \times (\text{first term} + \text{last term}) \]
where \( n \) is the number of terms in the series.
1. **First Term (a):** 37
2. **Last Term (l):** 104
3. **Number of Terms (n):**
\[ n = \text{last term} - \text{first term} + 1 \]
\[ n = 104 - 37 + 1 = 68 \]
4. **Sum Calculation:**
\[ \text{Sum} = \frac{n}{2} \times (a + l) \]
\[ \text{Sum} = \frac{68}{2} \times (37 + 104) \]
\[ \text{Sum} = 34 \times 141 \]
\[ \text{Sum} = 4794 \]
Thus, the sum of the series from 37 to 104 is **4794**.](https://content.bartleby.com/qna-images/question/31b55198-299b-40af-822f-8536b91cff39/81251c1c-85bf-42c8-9fda-2a0ef1fd33ff/b6ho14_reoriented.jpeg)
Transcribed Image Text:### Summation Problem
#### Problem Statement:
Find the sum \( 37 + 38 + 39 + 40 + \ldots + 103 + 104 \).
#### Answer Box:
The sum is \[ \_\_\_\_\_\}.
#### Instructions:
Enter your answer in the answer box and then click "Check Answer".
---
#### Explanation:
In this problem, we are asked to find the sum of a sequence of consecutive integers starting from 37 and ending at 104.
To solve this, we can use the formula for the sum of an arithmetic series:
\[ \text{Sum} = \frac{n}{2} \times (\text{first term} + \text{last term}) \]
where \( n \) is the number of terms in the series.
1. **First Term (a):** 37
2. **Last Term (l):** 104
3. **Number of Terms (n):**
\[ n = \text{last term} - \text{first term} + 1 \]
\[ n = 104 - 37 + 1 = 68 \]
4. **Sum Calculation:**
\[ \text{Sum} = \frac{n}{2} \times (a + l) \]
\[ \text{Sum} = \frac{68}{2} \times (37 + 104) \]
\[ \text{Sum} = 34 \times 141 \]
\[ \text{Sum} = 4794 \]
Thus, the sum of the series from 37 to 104 is **4794**.
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