= Let An= a₁ + a2 + ... + an, Bn=b₁ + b₂ + b3 + +bmDn C + C₂+...+c, and cn=a1bn + a₂bn-1+...+ab₁ne N. Using Cn mathematical induction, prove that ... = (a) DnaBn+ a₂Bn-1 +.... + a,B₁=b₁An + b₂A-1 + +bA₁ VEN (b) D₁ + D₂+...+D=A₁Bn+A₂B-1 + ... + AB₁ VnE N

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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Let An= a₁ + a₂ + ... + an, B₂=b₁ + b₂ + b3 +
+an, B₂=b₁ + b₂ + b3 + ... + b₂ D₂ = C₁
and cn=abn + a₂bn-1+...+ab₁ne N. Using
induction, prove that
Cn
.+a,B₁=b₁An + b₂An-1 +...
(a) Dn=a₁Bn+ a₂Bn-1 + ...
+b,A1VneN
+ C₂+...+c,
mathematical
(b) D₁ + D₂+...+ D₂ = A₁B₁ + A₂Bn-1 + ... + A₂B₁ ne N
n
Transcribed Image Text:Let An= a₁ + a₂ + ... + an, B₂=b₁ + b₂ + b3 + +an, B₂=b₁ + b₂ + b3 + ... + b₂ D₂ = C₁ and cn=abn + a₂bn-1+...+ab₁ne N. Using induction, prove that Cn .+a,B₁=b₁An + b₂An-1 +... (a) Dn=a₁Bn+ a₂Bn-1 + ... +b,A1VneN + C₂+...+c, mathematical (b) D₁ + D₂+...+ D₂ = A₁B₁ + A₂Bn-1 + ... + A₂B₁ ne N n
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