3. Use mathematical induction to prove the following statements.(e) For any n E N\{0},7-85531(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},nr=1ar = 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.

As per the guideline I am answering only first question as they are different questions. We have to…

Answered: (e) For any n €N\{0}, D-C Στις r=1 VI 1…

Math

Advanced Math

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 56E

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Question

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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