Problem 5.5 Prove that for every positive integer n, 1 1+ V2' V3 1 +...+ Vn 1 > 2(Vn+1- 1)
Problem 5.5 Prove that for every positive integer n, 1 1+ V2' V3 1 +...+ Vn 1 > 2(Vn+1- 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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![**Problem 5.5**
Prove that for every positive integer \( n \),
\[
1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} > 2(\sqrt{n+1} - 1)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07a7d798-02df-4f9b-9ae9-e3ac676193b7%2F39c9b219-f248-4397-a39e-964136db2c7d%2F6ohm96l_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 5.5**
Prove that for every positive integer \( n \),
\[
1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} > 2(\sqrt{n+1} - 1)
\]
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