Suppose that {b} = 0 ∞ and {c} = 0° n n n'n satisfy the recurrence relations and initial conditions b n+1 C n+1 = 3b + 2c +1,b = 4 n n = 5b - 7c + n,c。 = -3 n n 0 Let B(x) be the generating function for the sequence {b} = 0°, that is 00 n n'n B(x) = Σ bx. Find a simple closed n = 0 bx n form expression (with no infinite sums) for B(x).
Suppose that {b} = 0 ∞ and {c} = 0° n n n'n satisfy the recurrence relations and initial conditions b n+1 C n+1 = 3b + 2c +1,b = 4 n n = 5b - 7c + n,c。 = -3 n n 0 Let B(x) be the generating function for the sequence {b} = 0°, that is 00 n n'n B(x) = Σ bx. Find a simple closed n = 0 bx n form expression (with no infinite sums) for B(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Transcribed Image Text:Suppose that {b}
= 0 ∞ and {c} = 0°
n n
n'n
satisfy the recurrence relations and initial
conditions
b
n+1
C
n+1
= 3b + 2c +1,b = 4
n
n
= 5b - 7c + n,c。 = -3
n
n
0
Let B(x) be the generating function for
the sequence {b} = 0°, that is
00
n
n'n
B(x) = Σ bx. Find a simple closed
n = 0
bx
n
form expression (with no infinite sums)
for B(x).
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