13 Select the value of the sum k=-2 O 3 O 19 O 14 0 9
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
![**Question:**
Select the value of the sum \( \sum_{k=-2}^{3} k^2 \).
**Options:**
- ○ 3
- ○ 19
- ○ 14
- ○ 9
**Explanation:**
This problem asks you to evaluate the sum of squares of integers from \( k = -2 \) to \( k = 3 \). To find the sum, calculate each term:
1. \( (-2)^2 = 4 \)
2. \( (-1)^2 = 1 \)
3. \( 0^2 = 0 \)
4. \( 1^2 = 1 \)
5. \( 2^2 = 4 \)
6. \( 3^2 = 9 \)
Now add these values together:
\[ 4 + 1 + 0 + 1 + 4 + 9 = 19 \]
Therefore, the value of the sum is 19.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58591baa-c0bc-433b-b6a8-54571afeaf18%2Fc2be5aea-318b-4d77-ab8c-911426bd0876%2Fwgo0erl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Select the value of the sum \( \sum_{k=-2}^{3} k^2 \).
**Options:**
- ○ 3
- ○ 19
- ○ 14
- ○ 9
**Explanation:**
This problem asks you to evaluate the sum of squares of integers from \( k = -2 \) to \( k = 3 \). To find the sum, calculate each term:
1. \( (-2)^2 = 4 \)
2. \( (-1)^2 = 1 \)
3. \( 0^2 = 0 \)
4. \( 1^2 = 1 \)
5. \( 2^2 = 4 \)
6. \( 3^2 = 9 \)
Now add these values together:
\[ 4 + 1 + 0 + 1 + 4 + 9 = 19 \]
Therefore, the value of the sum is 19.
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