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Description: 4.Define the sequence an by a, = 1, a, = 33, and an =3an-1+ 10an-2 for n 2 3. Prove that an = 5" – (-2)n+1for all n 2 1.

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4. Define the sequence an by a, = 1, a, = 33, and an = 3an-1+ 10an-2 for n 2 3. Prove that an = 5" – (-2)n+1 for all n 2 1.

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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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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4.
Define the sequence an by a, = 1, a, = 33, and an =
3an-1+ 10an-2 for n 2 3. Prove that an = 5" – (-2)n+1
for all n 2 1.

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