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QUESTION
let a1 = 2, a(n+1) = (5*a(n) - 4) / a(n) for n=1.
let a1 = 2, a(n+1) = (5*a(n) - 4) / a(n) for n>=1. Show that (1 <= a(n) <= a(n+1) <= 4) for n>=1
Given,A(n+1) = 5*A(n) -4/A(n) A(n+1) = 5 – [4/A(n)]That can be written as[A(n+1) – 1]/4 = 1 – [1/A(n)]Putting A(1) = 2A(2)> 1From A(2) ,A( 3) >1This tells that A(n) > 1A(n+1)...