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Let ao 1 and an 2an-1 + 1 for every n ≥ 1. Let G(r) be the generating function of the sequence ao, a1, a2,.... = (i) Multiply both sides of an = 2an-1 + 1 by x", add those up from n = 1 to infinity. By using Σox² = 1/(1- x) for |x| < 1, find a closed formula for G(x).

Let ao 1 and an 2an-1 + 1 for every n ≥ 1. Let G(r) be the generating function of the sequence ao, a1, a2,.... = (i) Multiply both sides of an = 2an-1 + 1 by x", add those up from n = 1 to infinity. By using Σox² = 1/(1- x) for |x| < 1, find a closed formula for G(x).

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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. Let ao = 1 and an = 2an-1 +1 for every n > 1. Let G(x) be the generating function of the sequence ao, a1, a2, . . .. (i) Multiply both sides of an = 2an-1+1 by x", add those up from n = 1 to infinity. By using E, " = 1/(1 – x) for |x| < 1, find a closed formula for G(r).
Transcribed Image Text:. Let ao = 1 and an = 2an-1 +1 for every n > 1. Let G(x) be the generating function of the sequence ao, a1, a2, . . .. (i) Multiply both sides of an = 2an-1+1 by x", add those up from n = 1 to infinity. By using E, " = 1/(1 – x) for |x| < 1, find a closed formula for G(r).
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