1. Solve the following recurrence relations by the method of generating functions. = a) an+1an 3", n≥0, ao = 1 - b) an+1 — an = n², n≥0, ao = ann², 1 c) an+23an+1+2an = 0, n≥0, ao = 1, a₁ = 6 d) an+22an+1 + An = · 2an+1+an = 2", n≥0, 2", n≥0, ao = 1, a₁ = 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 54E
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1. Solve the following recurrence relations by the method of
generating functions.
a) an+1 an = 3", n≥0, ao = 1
-
b) an+1
-
— an = n², n ≥0, ao
= 1
c) an+2
-
Зап+1
3an+1+2an = 0, n≥0, ao =
1,
α
a₁ = 6
-
d) an+2 − 2an+1+an = 2", n≥0, ao =
1,
a₁ = 2
Transcribed Image Text:1. Solve the following recurrence relations by the method of generating functions. a) an+1 an = 3", n≥0, ao = 1 - b) an+1 - — an = n², n ≥0, ao = 1 c) an+2 - Зап+1 3an+1+2an = 0, n≥0, ao = 1, α a₁ = 6 - d) an+2 − 2an+1+an = 2", n≥0, ao = 1, a₁ = 2
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