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(e) For any n €N\{0}, D-C Στις r=1 VI 1 - η 2 11

(e) For any n €N\{0}, D-C Στις r=1 VI 1 - η 2 11

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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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.
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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