Use the product notation to rewrite the following expression. (7-t)-(7-t²). (7-³). (7-4) (7-5) = 5
Use the product notation to rewrite the following expression. (7-t)-(7-t²). (7-³). (7-4) (7-5) = 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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![**Use the product notation to rewrite the following expression.**
\[
(7 - t) \cdot (7 - t^2) \cdot (7 - t^3) \cdot (7 - t^4) \cdot (7 - t^5) = \prod_{k=1}^{5} (\text{ })
\]
**Explanation:**
The expression on the left is a product of five terms, each of the form \((7 - t^k)\) where \(k\) ranges from 1 to 5. The right side of the equation uses product notation (also known as Pi notation) to represent this product compactly.
The product notation \(\prod_{k=1}^{5}\) indicates that you multiply the terms obtained by substituting \(k\) into the expression provided. Therefore, the expression inside the box should reflect the general form of the terms being multiplied, which is \((7 - t^k)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fb91a413b-7896-4623-886c-d25d73caae15%2F3b5o9qp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Use the product notation to rewrite the following expression.**
\[
(7 - t) \cdot (7 - t^2) \cdot (7 - t^3) \cdot (7 - t^4) \cdot (7 - t^5) = \prod_{k=1}^{5} (\text{ })
\]
**Explanation:**
The expression on the left is a product of five terms, each of the form \((7 - t^k)\) where \(k\) ranges from 1 to 5. The right side of the equation uses product notation (also known as Pi notation) to represent this product compactly.
The product notation \(\prod_{k=1}^{5}\) indicates that you multiply the terms obtained by substituting \(k\) into the expression provided. Therefore, the expression inside the box should reflect the general form of the terms being multiplied, which is \((7 - t^k)\).
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