12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2, a, = 2a,-1 - an-2 + 2. (a) Find a2, a3, a4 and as. (b) Conjecture a formula for a, Vn e NU{0}. (c) Prove your conjecture from (b). %3D
12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2, a, = 2a,-1 - an-2 + 2. (a) Find a2, a3, a4 and as. (b) Conjecture a formula for a, Vn e NU{0}. (c) Prove your conjecture from (b). %3D
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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Transcribed Image Text:12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and
for n > 2, a, = 2a,-1 - an-2 + 2.
(a) Find a2, a3, a4 and as.
(b) Conjecture a formula for a, Vn e NU{0}.
(c) Prove your conjecture from (b).
%3D
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