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**Sequences / Real Analysis question**

## Homework Statement

a,b are the roots of the quadratic equation x

^{2}- x + k = 0, where 0 < k < 1/4.

(Suppose a is the smaller root). Let h belong to (a,b). The sequence x

_{n}is defined by:

[tex]x_1 = h, x_{n+1} = x^2_n + k. [/tex]

Prove that a < x

_{n+1}< x

_{n}< b, and then determine the limit of x

_{n}.

## Homework Equations

## The Attempt at a Solution

I have no idea how to start, if you could help me.

Thanks.

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