bjr
A
1 + 1/2 = 3/2
1 + 1/3 = 4/3
- - - -
(1 + 1/8) = 9/8
(1 + 1/9) = 10/9
A = (3/2) x (4/3) x 5/4) x (6/5) x (7/6) x (8/7) x (9/8) x (10/9)
on simplifie, il reste 10/ 2 = 5
A = 5
B
1 - 1/2 = 1/2
1 - 1/3 = 2/3
- - - - -
1 - 1/8 = 7/8
1-1/9 = 8/9
B = (1/2) x (2/3) x (3/4) x (4/5) x (5/6) x (6/7) x (7/8) x (8/9)
on simplifie, il reste 1/9
B = 1/9
P
(1 + 1/2)(1 - 1/2) = 1 - 1/4
(1 + 1/3)(1 - 1/3) = 1 - 1/9 etc.
P est le produit de A par B
P = 5 x 1/9 = 5/9
P = 5/9
