Compute the product. 9 II = 3 i(i + 2) (i − 1) (i+1) ||
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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![### Compute the Product
Compute the product:
\[
\prod_{i=3}^{9} \frac{i(i + 2)}{(i - 1) \cdot (i + 1)}
\]
The expression is asking to calculate the product of the terms \(\frac{i(i + 2)}{(i - 1) \cdot (i + 1)}\) as \(i\) ranges from 3 to 9.
**Explanation of the Product Notation:**
- The symbol \(\prod\) stands for "product", similar to how \(\sum\) stands for "summation".
- The expression below \(\prod\) indicates the starting value of \(i\) (in this case, \(i = 3\)).
- The number above \(\prod\) indicates the ending value of \(i\) (in this case, \(i = 9\)).
- For each integer value of \(i\) from 3 to 9, calculate the term \(\frac{i(i + 2)}{(i - 1) \cdot (i + 1)}\) and multiply all such terms together.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fe58b147a-17ae-448b-8345-6fc2bd5711cc%2F50wpi49_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Compute the Product
Compute the product:
\[
\prod_{i=3}^{9} \frac{i(i + 2)}{(i - 1) \cdot (i + 1)}
\]
The expression is asking to calculate the product of the terms \(\frac{i(i + 2)}{(i - 1) \cdot (i + 1)}\) as \(i\) ranges from 3 to 9.
**Explanation of the Product Notation:**
- The symbol \(\prod\) stands for "product", similar to how \(\sum\) stands for "summation".
- The expression below \(\prod\) indicates the starting value of \(i\) (in this case, \(i = 3\)).
- The number above \(\prod\) indicates the ending value of \(i\) (in this case, \(i = 9\)).
- For each integer value of \(i\) from 3 to 9, calculate the term \(\frac{i(i + 2)}{(i - 1) \cdot (i + 1)}\) and multiply all such terms together.
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