session 2008 OLYMPIADES ACADÉMIQUES DE MATHÉMATIQUES

2 = 1 + 1 1
1+1 16= 1
3 = 1 + 2 1
1+1 26= 1
3=1+1+1 1
1+1 1+1 16= 1
n2n+ 2 2n+ 9
x

A B
C
C
R
AMNB
R
R ABC
AB = 9cm AC = 15cm
BC = 13cm
ABC M
N R
i j
C(i, j)C(3,4) = 18
C(1,9) C(1,10) C(1,13) C(1, j + 1) C(1, j)
C(9,1) C(10,1) C(13,1) C(i+ 1,1) C(i, 1)
C(1, j + 1) C(1, j)C(i+ 1,1) C(i, 1)
C(1, j)j C(i, j)i j
1 + 2 + · · · +n=n(n+1)
2
i j C(i, j) = 2008