Let (an) be a sequence satisfying the equation: 0; a₂ = 1 a1 = an+2 = z(an+1+2an). Show that the sequence (an) converges

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Let An Be A Sequence Satisfying The Equation 0 A 1 A1 An 2 Z An 1 2an Show That The Sequence An Converges 1 (24.37 KiB) Viewed 26 times

Let (an) be a sequence satisfying the equation: 0; a₂ = 1 a1 = an+2 = z(an+1+2an). Show that the sequence (an) converges. We will do it in steps: a) Show that an an+1 for any n. b) Show that if and 1 an+1 ≤ an an+1 ≤an+2 ≤ an an+1 anan+1 ≥ an+2 ≥ an