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the sum of

the sum of

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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(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, bare in arithmetic progression a, G₁,G2, b are in geometric and a, H₁, H₂, bare in harmonic progression progression then show that G1 G₂ A1 + A2 H₁ H₂ H₁ + H ₂ H2 = (b) Find the sum of (2a + b)(a +26) 9ab 2 1 1 1+2[1 + ²) + 3 (1 + ² + 50 .50-terms
Transcribed Image Text:(a) Let a and b be positive real numbers. If a, A₁, A₂, bare in arithmetic progression a, G₁,G2, b are in geometric and a, H₁, H₂, bare in harmonic progression progression then show that G1 G₂ A1 + A2 H₁ H₂ H₁ + H ₂ H2 = (b) Find the sum of (2a + b)(a +26) 9ab 2 1 1 1+2[1 + ²) + 3 (1 + ² + 50 .50-terms
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