# 2018-01 Recurrence relation

Define a sequence $$\{ a_n \}$$ by $$a_1 = a$$ and
$a_n = \frac{2n-1}{n-1} a_{n-1} -1$
for $$n \geq 2$$. Find all real values of $$a$$ such that $$\lim_{n \to \infty} a_n$$ exists.

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