Bonsoir sil vous plait aidee moi pour faire cette exercice

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