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(a) State the definition of a (k +1)-term linear recurrence relation. (b) Let (F(n))n20 be a sequence that satisfies the recurrence relation F(n) = 4F(n – 1) – 3F(n – 2) for n> 2 with initial conditions F(0) = 2 and F(1) = 4. Find the solution to the recurrence relation – a closed form expression for F(n). | (c) If (F(n))n>o is a sequence, write down the generating function for (F(n))n>0-

(a) State the definition of a (k +1)-term linear recurrence relation. (b) Let (F(n))n20 be a sequence that satisfies the recurrence relation F(n) = 4F(n – 1) – 3F(n – 2) for n> 2 with initial conditions F(0) = 2 and F(1) = 4. Find the solution to the recurrence relation – a closed form expression for F(n). | (c) If (F(n))n>o is a sequence, write down the generating function for (F(n))n>0-

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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2. (a) State the definition of a (k + 1)-term linear recurrence relation. (b) Let (F(n))n>o be a sequence that satisfies the recurrence relation F(n) — 4F(n — 1) — ЗF(n — 2) for n > 2 with initial conditions F(0) = 2 and F(1) = 4. Find the solution to the recurrence relation – a closed form expression for F(n). (c) If (F(n))n>o is a sequence, write down the generating function for (F(n))n>0- (d) Suppose that (F(n))n>0 is a sequence that satisfies the recurrence relation F(n) = 3F(n – 1) + 10F(n – 2) for n> 2 and with initial conditions F(0) = -1 and F(1) = 9, use the technique of generating functions to find a closed form for F(n) for n > 0.
Transcribed Image Text:2. (a) State the definition of a (k + 1)-term linear recurrence relation. (b) Let (F(n))n>o be a sequence that satisfies the recurrence relation F(n) — 4F(n — 1) — ЗF(n — 2) for n > 2 with initial conditions F(0) = 2 and F(1) = 4. Find the solution to the recurrence relation – a closed form expression for F(n). (c) If (F(n))n>o is a sequence, write down the generating function for (F(n))n>0- (d) Suppose that (F(n))n>0 is a sequence that satisfies the recurrence relation F(n) = 3F(n – 1) + 10F(n – 2) for n> 2 and with initial conditions F(0) = -1 and F(1) = 9, use the technique of generating functions to find a closed form for F(n) for n > 0.
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