Réponse :

1 + 1/2 + 1/(1 + 1/2) + 1/(1 + 1/(1 + 1/2) = 3/2 + 2/3 + 3/5 = 45/30 + 20/30 + 18/30

= 83/30

1 + 1/2 = 3/2

1/(1 + 1/2) = 1/3/2 = 2/3

1/(1 + 1/(1 + 1/2) = 1/(1 + 2/3) = 1/5/3 = 3/5  

Explications étape par étape :

Salut !

1+1/2 + 1/ 1+1/2 + 1/1+1/1+1:2

=> 1+1/2 = 2/2+1/2 = 3/2

=> 1/1+1:2 = 1/3/2= 1×2/3 = 2/3

=> 1/1 +1/1+1:2 = 1/1+2/2+1:2=1/1+3:2=1/5:2

1/5:2 = 1×2/5 = 2/5

=> 3/2 + 2/3 + 2/5 =>

45/30+20/30+12/30 = 87/30

Bonne soirée.