Root sequence question

bomba923

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] ??

bomba923	Root sequence question Tweet 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] ??