13. Calculate (k-j). j=2 k=5
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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![**13. Calculate**
\[
\sum_{j=2}^{4} \sum_{k=5}^{8} (k - j).
\]
This expression involves a double summation. Here's a detailed breakdown:
- **Outer Summation**: \( \sum_{j=2}^{4} \) indicates that the variable \( j \) runs from 2 to 4.
- **Inner Summation**: \( \sum_{k=5}^{8} (k - j) \) indicates that for each value of \( j \), the variable \( k \) runs from 5 to 8.
To solve this, calculate the inner summation for each \( j \) from 2 to 4, and then sum these results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cef3050-b0aa-40af-9112-57cab04a18ba%2F104609ee-d8e0-4c30-9466-b4d59d5f0b7b%2F8nx0rn9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**13. Calculate**
\[
\sum_{j=2}^{4} \sum_{k=5}^{8} (k - j).
\]
This expression involves a double summation. Here's a detailed breakdown:
- **Outer Summation**: \( \sum_{j=2}^{4} \) indicates that the variable \( j \) runs from 2 to 4.
- **Inner Summation**: \( \sum_{k=5}^{8} (k - j) \) indicates that for each value of \( j \), the variable \( k \) runs from 5 to 8.
To solve this, calculate the inner summation for each \( j \) from 2 to 4, and then sum these results.
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The given series is a finite series we can solve this by expanding.
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