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. Then
My Solution::
Then
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))}_{n-times} = )
For a slightly different way of looking at it, you might notice that the n'th iterateis given by
where
is the n'th Fibonacci number. This is given by the formula
where
and
But
, and so
as
Thus for large values of n,
and therefore
}(x) \approx\frac{\lambda_+^nx+\lambda_+^{n+1}}{\lambda _+^{n+1}x+\lambda_+^{n+2}} = \frac1\lambda_+ = \frac2{1+\sqrt5} = \tfrac12(\sqrt5-1).)
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