Prove that the sequence is increasing.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Prove that the sequence is increasing. Actually this is a bit hard, but proceed as
follows.
1
(1+:)"/(1+)
n+1
• Note that an
Hence, use algebra to show that
n
n
n+1
(),
An+1
1
1 +
(n + 1)²,
An
• Bernoulli's inequality states that for any x> -1, (1+x)n > 1+ nx. Use this to
deduce that
An+1
> (1
An
n +1
(;+)(4"-)
and simplify the last expression.
Expert Solution
Step 1
In this question, we have given a sequence
To prove the sequence is increasing by a given method.
Step by step
Solved in 2 steps with 1 images
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