Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn = 2 E žn-h h=0 h=1 Substituting (6) in (5), we have E Zn-h 1 kn-11 h=1 kn+1 Zn Vn (7) 2 Wn-p 1 = Vn-1. Vn+1 Wn - l kn Hence, we see that 1 ki = 1 V1 = ko wo - H 20 - € ko W-1 + w_2 Vo = Z-1 + 2-2 and at n = 1, k2 = ko and V2 = Vo, at n = 2, k3 = k1 and V3 = V1, at n = 3, k4 = ko and V4 = Vo, at n = 4, ks = k and V5 = V1, (8) at n = 2 n, k2n = ko and V2n = Vo, at n = 2n+ 1, k2n+1 = k1 and V2n+1 = V1. Now, from the relations in (6) we get Wn = u + kn (Wn-1 + Wn-2) and zn = € + Vn (žn-1 + Zn-2). (9) Using (8) in (9), we have W2n = H + ko (W2n-1 + W2n-2), W2n+1 = l + kı (w2n + W2n-1), (10) 22n = € + vo (22n-1 + 22n-2), 22n+1 = € +vi (22n + 22n-1). 介
Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn = 2 E žn-h h=0 h=1 Substituting (6) in (5), we have E Zn-h 1 kn-11 h=1 kn+1 Zn Vn (7) 2 Wn-p 1 = Vn-1. Vn+1 Wn - l kn Hence, we see that 1 ki = 1 V1 = ko wo - H 20 - € ko W-1 + w_2 Vo = Z-1 + 2-2 and at n = 1, k2 = ko and V2 = Vo, at n = 2, k3 = k1 and V3 = V1, at n = 3, k4 = ko and V4 = Vo, at n = 4, ks = k and V5 = V1, (8) at n = 2 n, k2n = ko and V2n = Vo, at n = 2n+ 1, k2n+1 = k1 and V2n+1 = V1. Now, from the relations in (6) we get Wn = u + kn (Wn-1 + Wn-2) and zn = € + Vn (žn-1 + Zn-2). (9) Using (8) in (9), we have W2n = H + ko (W2n-1 + W2n-2), W2n+1 = l + kı (w2n + W2n-1), (10) 22n = € + vo (22n-1 + 22n-2), 22n+1 = € +vi (22n + 22n-1). 介
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 50E
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