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Show that if p q, then the formula: (3)* – 1 Ar fulfills the recursion formula - A =p. A+1 + q- A4-1, om 1

Show that if p q, then the formula: (3)* – 1 Ar fulfills the recursion formula - A =p. A+1 + q- A4-1, om 1

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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Show that if p q, then the formula: (2)*- (2)" Ar at6 fulfills the recursion formula - A=p A+1 +4 A-1, om 1<k<a+b, Use q = 1-p in the calculations. 2. In the future you should assume that p = q = (%) (odds when flipping a coin) The expression for Ak in question 1 cannot be used, why? we should therefore guess a explicit formula that can be used, in this case by calculations. Observe that we now have the following recursive connection: A = Ak+1 AR-1, 1<k<a+b, Ao = 0, och Aatb= 1. Example: by chosing a=2 and b=1, therefore A_3= A_a+b = 1, Az = As + A1, A2 A3+ · A2 3 · A3, 2 4 1 2 112
Transcribed Image Text:Show that if p q, then the formula: (2)*- (2)" Ar at6 fulfills the recursion formula - A=p A+1 +4 A-1, om 1<k<a+b, Use q = 1-p in the calculations. 2. In the future you should assume that p = q = (%) (odds when flipping a coin) The expression for Ak in question 1 cannot be used, why? we should therefore guess a explicit formula that can be used, in this case by calculations. Observe that we now have the following recursive connection: A = Ak+1 AR-1, 1<k<a+b, Ao = 0, och Aatb= 1. Example: by chosing a=2 and b=1, therefore A_3= A_a+b = 1, Az = As + A1, A2 A3+ · A2 3 · A3, 2 4 1 2 112
Az = As + ( A2), 3. 1 A2 4. 4 1 Az = 2 Az = 3 2 3. 1 2 A2 23 1 A = 3 by choosing a and b to different bigger values its possible to guess what A1 and Ak will be for general k, 1.
Transcribed Image Text:Az = As + ( A2), 3. 1 A2 4. 4 1 Az = 2 Az = 3 2 3. 1 2 A2 23 1 A = 3 by choosing a and b to different bigger values its possible to guess what A1 and Ak will be for general k, 1.
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