4. A sequence of numbers xo, x1, x2,... is such that xo have: In Xp = 1 2 Xn-1 + 2. MONIO n- In = ar + 2 (1+r + r² + . . . + p²−1). 3 and, for each n ≥ 1, we Show that I can be written in the following form, for some numbers a and r (which you should find): Hence, or otherwise, find an explicit expression for x, in terms of n, simplifying your answer as far as possible. Hence describe the behaviour of xn as n →∞.
4. A sequence of numbers xo, x1, x2,... is such that xo have: In Xp = 1 2 Xn-1 + 2. MONIO n- In = ar + 2 (1+r + r² + . . . + p²−1). 3 and, for each n ≥ 1, we Show that I can be written in the following form, for some numbers a and r (which you should find): Hence, or otherwise, find an explicit expression for x, in terms of n, simplifying your answer as far as possible. Hence describe the behaviour of xn as n →∞.
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:4. A sequence of numbers xo, x1, x2,... is such that xo
have:
In
Xp =
1
2
Xn-1 + 2.
MONIO
n-
In = ar + 2 (1+r + r² + . . . + p²−1).
3 and, for each n ≥ 1, we
Show that I can be written in the following form, for some numbers a and r (which
you should find):
Hence, or otherwise, find an explicit expression for x, in terms of n, simplifying
your answer as far as possible. Hence describe the behaviour of xn as n →∞.
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