Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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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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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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