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> The sequence $\{a\_n\}$ is determined by $$a\_1 = 1, a\_{n+1} = \frac{3n-1}{3n} a\_n + \frac{1}{n^2}, \quad \forall n\ge 1.$$
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> Find the limit of $\{a\_n\}$ (if it exists).
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I guess the limit is $0$ by using MATLAB, but the sequence converges really slowly.