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 November 15th, 2010, 06:59 AM #1 Member   Joined: Oct 2010 Posts: 43 Thanks: 0 NICE-HELP Let a be a postive real number. Let $(x_n) (n=1,2,...,)$ be a sequence defined by $x_1=a,\ x_{n+1}=\frac{x_n.\sqrt{2+\sqrt{2}+....+\sqrt{2}}} {x_n+1}$ for all $n=1,2,.$...(there are exactly n numbers 2 in the numerator). Prove that the sequence ($x_n) \,(n=1,2,...)$ has a finite limit and find thís limit.
 November 15th, 2010, 09:55 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,250 Thanks: 1439 To what depth are the square roots in the numerator nested?

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