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1. Derive the generating function A for a series a, if a, is defined recursively as a, = an-1-2a,-a and ao = -1, aj = 2. Show that if we use the reverse of the recurrence relation, i.c. A-an-1A+2a,-2A², terms will cancel and this equals 1. By finding the solution to the recurrence relation, derive a closed formula for the sequence.

1. Derive the generating function A for a series a, if a, is defined recursively as a, = an-1-2a,-a and ao = -1, aj = 2. Show that if we use the reverse of the recurrence relation, i.c. A-an-1A+2a,-2A², terms will cancel and this equals 1. By finding the solution to the recurrence relation, derive a closed formula for the sequence.

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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1. Derive the generating function A for a series a, if a, is defined recursively as an = an-1-2a,-2 and ao = -1, a1 = 2. Show that if we use the reverse of the recurrence relation, i.e. A-an-1A+2an-2A?, terms will cancel and this equals 1. By finding the solution to the recurrence relation, derive a closed formula for the sequence. (NOTE: Please elaborate on the answer and explain. Please do not copy-paste the answer from the internet or from Chegg.)
Transcribed Image Text:1. Derive the generating function A for a series a, if a, is defined recursively as an = an-1-2a,-2 and ao = -1, a1 = 2. Show that if we use the reverse of the recurrence relation, i.e. A-an-1A+2an-2A?, terms will cancel and this equals 1. By finding the solution to the recurrence relation, derive a closed formula for the sequence. (NOTE: Please elaborate on the answer and explain. Please do not copy-paste the answer from the internet or from Chegg.)
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