Let f a continue function acknowleding α as a fix point on [0,1].F a function such as (dF/dx)=f(x) ∀ n , u_(n+1) =((F(u_n )−F(α))/(u_n −α)) Prove that lim_(n→∞) u


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Question Number 86326 by ~blr237~ last updated on 28/Mar/20

$L e t f a c o n t i n u e f u n c t i o n a c k n o w l e d i n g$ $α a s a f i x p o i n t o n [0, 1] . F a f u n c t i o n s u c h a s \frac{d F}{d x} = f (x)$ $\forall n, u_{n + 1} = \frac{F (u_{n}) - F (α)}{u_{n} - α}$ $P r o v e t h a t \lim_{n \to \infty} u_{n} = α$
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