Define a sequence of functions f₀, f₁, f₂, ......, by

f₀(x)= 8, for all real x, and
f_n+1(x) = sqrt(x² + 6f_n(x)); for all real x and all non-negative integers n.

Solve the equation

f_n(x)= 2x

(In reply to re(3): Solution? by Richard)

x=4 appears to be the only solution for any integer n.  I don't know what a non-recursive definition of this sequence would be, but just by observation (using Excel) each of the values of f_n(x) converge rapidly to a limit as n goes to infinity, none of which is equal to 2x.

Posted by tomarken on 2006-11-19 16:04:04