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Question 3 (a) Define a sequence {a,} as follows: Let a, = 1, and define (a,)? + (2n + 3)a, + (4n + 3) an+2 an+1 for n 21. Use Mathematical Induction to show that n sa, s (n+ 1)? for all positive integers n.

Question 3 (a) Define a sequence {a,} as follows: Let a, = 1, and define (a,)? + (2n + 3)a, + (4n + 3) an+2 an+1 for n 21. Use Mathematical Induction to show that n sa, s (n+ 1)? for all positive integers n.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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plz solve ques 3 part a and c 

Question 3 (a) Define a sequence {an} as follows: Let az = 1, and define (an)? + (2n + 3)an + (4n + 3) an+1 an + 2 for n 2 1. Use Mathematical Induction to show that n? s an < (n+ 1)? for all positive integers n. (b) Use the Euclidean Algorithm to find d = ged(4753,1379) and express d as an integral linear combination of 4753 and 1379. (c) Let a, b,c be non-zero integers. Suppose that x, y are integers such that ax + by = c. (i) Show that for any integer z, zb a(x- god(a.b) + b (y +pod(a.) = c. gcd(a, b) Suppose that r, s are integers (possibly different from x,y respectively) such that ar + bs = c. Show that there exists some integer w such that (ii) wb wa r =x- and s= y + gcd(a,b) gcd(a, b)
Transcribed Image Text:Question 3 (a) Define a sequence {an} as follows: Let az = 1, and define (an)? + (2n + 3)an + (4n + 3) an+1 an + 2 for n 2 1. Use Mathematical Induction to show that n? s an < (n+ 1)? for all positive integers n. (b) Use the Euclidean Algorithm to find d = ged(4753,1379) and express d as an integral linear combination of 4753 and 1379. (c) Let a, b,c be non-zero integers. Suppose that x, y are integers such that ax + by = c. (i) Show that for any integer z, zb a(x- god(a.b) + b (y +pod(a.) = c. gcd(a, b) Suppose that r, s are integers (possibly different from x,y respectively) such that ar + bs = c. Show that there exists some integer w such that (ii) wb wa r =x- and s= y + gcd(a,b) gcd(a, b)
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