(e) For any n €N\{0}, D-C Στις r=1 VI 1 - η 2 11
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Use mathematical induction to prove the following statements.
(e) For any n E N\{0},
7-8553
1
(g) Let f(x) = 1+x².
r=1
(f) Let a₁ = 1 and a2 = 1. Define an = an−1+ an−2 when n ≥ 3. Then for all n ≤ N\{0},
n
r=1
ar = an+2 1.
Then for any n € N,
(1 + x²) ƒ(n+²)(x) + 2(n + 2)x f(n+¹) (x) + (n + 2)(n + 1) ƒ(¹) (x) = 0.
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