I submitted question number 4 early but was hoping to get some clarification for further proof. I have to prove that f(n) is equal to that for all n 4) Define f : N-R as follows:f(1) = 3, f(2)and for n 2 3 f(n)2'f(n- 1) + f(n-2)Prove that f(n) = 2+ (-)"-1 for all n E N11+ - + •..41.<2 Vn e N5) Prove that 1+2n-1x + y6) Let x > 0 and y > 0, prove that ry <

Name: I submitted question number 4 early but was hoping to get some clarifi
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Description: I submitted question number 4 early but was hoping to get some clarification for further proof. I have to prove that f(n) is equal to that for all n 4) Define f : N-R as follows:f(1) = 3, f(2)and for n 2 3 f(n)2'f(n- 1) + f(n-2)Prove that f(n) = 2+ (

Answered: 4) Define f: N→R as follows: f(1) = 3,…

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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I submitted question number 4 early but was hoping to get some clarification for further proof. I have to prove that f(n) is equal to that for all n

4) Define f : N-R as follows:
f(1) = 3, f(2)
and for n 2 3 f(n)
2'
f(n- 1) + f(n-2)
Prove that f(n) = 2+ (-)"-1 for all n E N
1
1
+ - + •..
4
1.
<2 Vn e N
5) Prove that 1+
2n-1
x + y
6) Let x > 0 and y > 0, prove that ry <

Expert Solution

Step 1

Consider the provided question,

According to you we have to solve only question no. (4).

(4)

$G i v e n, f (1) = 3, f (2) = \frac{3}{2} a n d f o r n ⩾ 3, f (n) = \frac{f (n - 1) + f (n - 2)}{2} W e h a v e t o p r o v e t h a t f (n) = 2 + {(- \frac{1}{2})}^{n - 1} f o r a l l n \in N$

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