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Let f : [a,b] → [a,b] be continuous. Define a sequence recursively by z1 = x1,...

Let f : [a,b] → [a,b] be continuous. Define a sequence recursively by z1 = x1, zn = f(zn−1) where x1 ∈ [a,b]. Show that if the sequence {zn} is convergent, then it must converge to a fixed point of f.

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