(2k+1)! > 10¹
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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How do you find k? Please show step by step.
![The expression in the image is:
\[
(2k + 1)! > 10^4
\]
Explanation:
- **(2k + 1)!**: Represents the factorial of \(2k + 1\). The factorial, denoted by an exclamation mark (!), is the product of all positive integers up to the given number. For example, \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).
- **10^4**: This is an exponential expression equivalent to 10,000.
The inequality states that the factorial of \(2k + 1\) is greater than 10,000. To solve for \(k\), you would need to find the smallest integer \(k\) such that \( (2k + 1)! \) satisfies the inequality.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93724627-c7b6-406b-9a00-d0dcd2c570ce%2Fd3a327ed-1c78-48cd-aba4-235e6976135a%2F7fxlqb_processed.png&w=3840&q=75)
Transcribed Image Text:The expression in the image is:
\[
(2k + 1)! > 10^4
\]
Explanation:
- **(2k + 1)!**: Represents the factorial of \(2k + 1\). The factorial, denoted by an exclamation mark (!), is the product of all positive integers up to the given number. For example, \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).
- **10^4**: This is an exponential expression equivalent to 10,000.
The inequality states that the factorial of \(2k + 1\) is greater than 10,000. To solve for \(k\), you would need to find the smallest integer \(k\) such that \( (2k + 1)! \) satisfies the inequality.
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