the sum of
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
(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb74d23d4-3dff-4316-81ab-a5816197c1b9%2F1b3b4eb9-8e01-44c0-9ca7-b77fdeb82576%2Fho7kp9f_processed.png&w=3840&q=75)
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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