Prove that 1/(2n) < [1 · 3 · 5 . ... · (2n – 1)]/(2 · 4 · .. 2n) whenever n is a positive integer.
Prove that 1/(2n) < [1 · 3 · 5 . ... · (2n – 1)]/(2 · 4 · .. 2n) whenever n is a positive integer.
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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Proof by mathematical induction.
![**Problem 24:**
Prove that
\[
\frac{1}{2n} \leq \frac{1 \cdot 3 \cdot 5 \cdot \cdots \cdot (2n - 1)}{2 \cdot 4 \cdot \cdots \cdot 2n}
\]
whenever \( n \) is a positive integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39b0ccf5-4135-4a1a-87f6-32eedae45509%2F2950f75b-7b63-4f63-a7bd-e16c8520b090%2F2c4opp8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 24:**
Prove that
\[
\frac{1}{2n} \leq \frac{1 \cdot 3 \cdot 5 \cdot \cdots \cdot (2n - 1)}{2 \cdot 4 \cdot \cdots \cdot 2n}
\]
whenever \( n \) is a positive integer.
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