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2COS X-I Sin x, Yna1 = 2cosxy, – Yn-1+ n21 and 0

2COS X-I Sin x, Yna1 = 2cosxy, – Yn-1+ n21 and 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 33E
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Question
(a) A sequence is defined by y, = 2, y, = 2cosx -isin x, %3D Yn+1 =2cos xy, - Yn-1• n21 and 0<xS- 2 %| (i) Use mathematical induction to prove that for n20. 3 y, =(cosx+isinx)" +(cosx-isinx)" 1 CO cos x +isinx)" + 2
Transcribed Image Text:(a) A sequence is defined by y, = 2, y, = 2cosx -isin x, %3D Yn+1 =2cos xy, - Yn-1• n21 and 0<xS- 2 %| (i) Use mathematical induction to prove that for n20. 3 y, =(cosx+isinx)" +(cosx-isinx)" 1 CO cos x +isinx)" + 2
Yn n-o (b) Hence, or otherwise, show that limn+1 = e*.
Transcribed Image Text:Yn n-o (b) Hence, or otherwise, show that limn+1 = e*.
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