et a and b be positive real numbers. If a, A₁, A2,1

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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Question

(a) 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} 

 

(b) Find the sum of 

                   1+2(1+\frac{1|50})+3(1+\frac{1|50})\power{2}+.....50-terms 

(a) 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
G1G2
H1 H2
(b) Find the sum of
A1 + A2
$1+2
(2a + b)(a + 2b)
9ab
2
1
1+2[1 + ²) + 3 (1 + 1)² +
50
50
+ .....50 - terms
Transcribed Image Text:(a) 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 G1G2 H1 H2 (b) Find the sum of A1 + A2 $1+2 (2a + b)(a + 2b) 9ab 2 1 1+2[1 + ²) + 3 (1 + 1)² + 50 50 + .....50 - terms
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