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Root sequence question
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bomba923
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1
Apr15-05, 12:20 AM
P: 736
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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