Corrigé

unn n ≥5
∀n∈N,(n≥5⇒un+1 =n+1+un)u5= 5+10 = 15
u6= 21 u7= 28 u8= 36 u9= 45
n= 5 n
un=5 15 =1 3
n= 6 n
un=6 21 =2 7
1
36=2 7
un=1
2n(n+ 1)
x7→ 1
2x(x+ 1) −3523
. . .
1
2×83 ×(83 + 1) = 3403 1 2×84 ×(84 + 1) = 3570
3570 −3403 = 167
1
2(AB +CD)×DA (DA)
1800m2
A(AMGD)AMGD A(AMGD) = 30x
A(MBCG) = 1800 −30X
30x= 1800 −30x
x=1800
2×30 = 30
x
x
x
900m210
500 =x 900
x=10×900
500 = 18
10 ×9
B
C D A B
E

x
EF GH
E F [AB] [BC]
(F E) (CA) (GH)//(CA)
(EF )//(GH)
(F G)//(EH)
EF GH
(EF )//(CA)
(CA)⊥(BD)
(BD)//(F H)
⇒(EF )⊥(F G)