arithmetic progression a,
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
Let a and b be positive real numbers . If a , A\index{1},A\index{2},b are
in arithmetic progression a, G\index{1},G\index{2}, b are in geometric
progression and a, H\index{1},H\index{2}, b are in harmonic progression
then show that
\frac{G\index{1}G\index{2}|H\index{1}H\index{2}}=\frac{A\index{1}+A\index{2}|H\index{1}+H\index{2}}=\frac{(2a+b)(a+2b)|9ab}
Transcribed Image Text:Let a and b be positive real numbers. If a, A₁, A2, b are
in arithmetic progression a, G₁, G₂, b are in geometric
progression and a, H₁, H₂, b are in harmonic progression
then show that
G��� G₂
H₁ H₂
=
A₁ + A₂
H₁ + H₂
(2a + b)(a + 2b)
9ab
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