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Evaluation spécifique dans la section européenne Anglais Mathématiques

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Evaluation spécifique dans la section européenne Anglais-Mathématiques Choose one of the two following exercises and solve it : Exercise 1: Let u be the sequence defined by ?? ?? ? += = + 12 1 0 1 0 nn uu u 1) Show that u is bounded by 0 and 2. 2) Prove that for every whole number n, 12 12 ? ?= nn u . 3) Has u a limit? OR Exercise 2: A, B, C and G are points such that 1?=Az ; 32 izB += ; 32 izC ?= ; 3=Gz . 1) Prove that G is the barycentre of (A;-1);(B;2);(C;2). 2) Prove that ABC is equilateral. 3) Compute CG CA zz zz ? ? . What can you deduce from this?

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Evaluation spécifique dans la section européenne Anglais-Mathématiques Choose oneof the two following exercises and solve it : Exercise 1: u10 0 Let u be the sequence defined by1 u1u#1 n#1n 2 1)Show that u is bounded by 0 and 2. 1 2)Prove that for every whole number n,u12%. n n%1 2 3)Has u a limit? OR Exercise 2: A, B, C and G are points such thatz1 %1;z12#i3 ;z12%i3;z13 . ABCG 1)Prove that G is the barycentre of (A;-1);(B;2);(C;2). 2)Prove that ABC is equilateral. z%z A C 3)What can you deduce from this?Compute . z%z G C