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Let a and b be positive real numbers. If a arithmetic progression a, G₁, G₂, b are in g ogression and a, H₁, H₂, b are in harmonic

Let a and b be positive real numbers. If a arithmetic progression a, G₁, G₂, b are in g ogression and a, H₁, H₂, b are in harmonic

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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Question

(a) Find the sum to infinity of the series 

            1-3x+5x\power{2}-7x\power{3}+....∞

where 0<|x|<1

(b)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} 

 

 

(a) Find the sum to infinity of the series 1-3x+5x² - 7x³ + .... ∞ where 0 < x < 1 (b)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 G₁ G₂ H₁ H₂ A₁ + A₂ H₁ + H₂ (2a + b)(a + 2b) 9ab
Transcribed Image Text:(a) Find the sum to infinity of the series 1-3x+5x² - 7x³ + .... ∞ where 0 < x < 1 (b)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 G₁ G₂ H₁ H₂ A₁ + A₂ H₁ + H₂ (2a + b)(a + 2b) 9ab
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