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all three questions please. thank you

Prove that for all n N, O <In < 1. Prove by induction that for all n EN, ER EQ. Prove that in} is convergent and find its lim



The goal of this exercise is to prove that [0, 1] nQ is not closed. Let In} be a recursive sequence defined by In+1 = -) for
0 0
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vust. Solution 2 X - let {n} be a recursive sequence given by anti (ant ) for na! and x31, Xn20 . a) To prove that each n ECODate: Now takti Xk+ = } (xv + =XXXX O X EQ Xx + EQ. ☆ ( xk+x) EQ — ЭХүн єa - - - This implies that XnEQ Prat ..t o .. hooo h

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all three questions please. thank you Prove that for all n N, O <In < 1....
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