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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
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 \( n \), \[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} > 2(\sqrt{n+1} - 1) \]
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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