let consider (u_n ) such as u_0 ∈]0;1[ and u_(n+1) =u_n −u_n ^2 1)Prove that lim_(n→∞) ^n (√u_n ) = 1 and that the convergence domain of Σu_n x^n is D=[−1;1[ 2) Prove that the one of Σu


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Question Number 126777 by snipers237 last updated on 24/Dec/20

$l e t c o n s i d e r (u_{n}) s u c h a s u_{0} \in] 0; 1 [a n d u_{n + 1} = u_{n} - u_{n}^{2}$ $1) P r o v e t h a t \lim_{n \to \infty}^{n} \sqrt{u_{n}} = 1 a n d t h a t t h e c o n v e r g e n c e d o m a i n o f Σ u_{n} x^{n}$ $i s D = [- 1; 1 [$ $2) P r o v e t h a t t h e o n e o f Σ u_{n}^{2} x^{n} i s I = [- 1; 1]$
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