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For the recursive sequence

[tex] R_n = x + \sqrt {x - \sqrt {R_{n - 2} } } [/tex]

[tex] R_0 = x = k^2 - k + 1 [/tex]

[tex] \forall k \in \mathbb{N},\;k > 1 [/tex]why does[tex] \mathop {\lim }\limits_{n \to \infty } R_n = k^2 [/tex]??

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# Root sequence question

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