Consider the following length-7 sequences defined for -3 <= n <= 3X[n]={3,-2,0,1,4,5,2}• Y[n]={0,7,1,-3,4,9,-2}• W[n]={-5,4,3,6,-5,0,1}• Find the following(a) u[n] = x[n] + y[n](b) v[n] = x[n]• w[n](c) s[n] = y[n] – w[n](d) r[n] = 4.5y[n]

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Answered: Consider the following length-7…

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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(d) Two sequences (ao, a1,..., an,...) and (bo, b₁,..., bn,...) are defined by: an+1 = bn+1 an +2bn 2an + bn Find the formulae for an and bn (in terms of n). ao = 1, bo = 2 and = for all n ≥ 0.
8. Suppose ao, a1, a2, ... is a sequence such that do = a₁ = 1 and, for n ≥ 1, an+1 = n(an + an-1). (a) [BB] Find a2, a3, a4, and a5. (b) Guess a formula for an, valid for n ≥ 0, and use mathematical induction to prove that your guess is ollo correct.
Find the recursive formula of the following sequence. (4, 10, 18, 28,...} O a a₁ = 4, an = an-1 + 2(n+1), for n ≥ 2 Ob a₁ = 4,a₁ = an−1 +2(n − 1), for n ≥ 2 Oc_a₁ = 4,a₁ = an + 2(n − 1), for n ≥ 2 с Od a₁ = 4,a₁ = an−1 +2(n − 1), for n ≥ 4
4
3. Compute ao, a1, a2, a3, a4 the of the following sequences. (a) ao = 2, an = 3an-1 for n > 1. (b) ao = -5, a, = an-1 +5 for n > 1. (c) ao = 0, an = an-1 +n for n > 1.
6. Let {n} and {yn} be the following sequences that repeat in cycles of four: n = 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, ... and Find (a) lim inf xn + lim inf Yn Yn = 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2... (b) lim inf(xn + Yn) (c) lim sup n + lim sup yn
Let {n} and {n} be real sequences. Show that if xn → x and yn →y then for all a, ß ER, axn + Byn → ax + By

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Consider the following length-7 sequences defined for -3 <=n <= 3 • X[n]={3,-2,0,1,4,5,2} • Y[n]={0,7,1,-3,4,9,-2} • W[n]={-5,4,3,6,-5,0,1} Find the following (a) u[n] = x[n] + y[n] (b) v[n] = x[n]• w[n] (c) s[n] = y[n] – w[n] (d) r[n] = 4.5y[n]