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x_{n+2}=1/12 x_{n+1}+1/2 x_{n}+1, limit

Source: 1989 Greece MO Grade XII p3

September 7, 2024
limitSequencesreal analysis

Problem Statement

Find the limit of the sequence xnx_n defined by recurrence relation xn+2=112xn+1+12xn+1x_{n+2}=\frac{1}{12}x_{n+1}+\frac{1}{2}x_{n}+1 where n=0,1,2,...n=0,1,2,... for any initial values x2,x1x_2,x_1.
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