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Turkey TST 1996 Problem 6, must have the limit 0

Source: Turkey TST 1996 Problem 6

September 28, 2011
limitalgebra proposedalgebra

Problem Statement

Determine all ordered pairs of positive real numbers (a,b)(a, b) such that every sequence (xn)(x_{n}) satisfying lim⁡n→∞(axn+1−bxn)=0\lim_{n \rightarrow \infty}{(ax_{n+1} - bx_{n})} = 0 must have lim⁡n→∞xn=0\lim_{n \rightarrow \infty} x_n = 0.
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