Réponses

2014-02-10T14:04:59+01:00
A) A = 1 + 1/(2+1/2)
or 2+1/2 = 2*2/2 + 1/2 = 4/2 + 1/2 (* signifie multiplié par)

A = 1 + 1/(4/2+1/2)
A = 1 + 1/(5/2)

or 1/(5/2) = (1/1) / (5/2) = 1/1 : 5/2 et diviser une fraction a/b par une fraction c/d revient à multipier la fraction a/b par l'inverse de c/d or l'inverse de c/d est d/c.
exemple 1/2 : 3/5 = 1/2 * 5/3 = 1*5 / 2*3 = 5/6
ici 1/1 : 5/2 = 1/1 * 2/5 = 2/5 donc 1/(5/2) = 1*2/5 = 2/5 donc
A = 1 + 2/5
A = 5/5 + 2/5
A = 7/5

B = 1 + 1/(2 + 1/(2 + 1/2))
B = 1 + 1/(2 + 1/(4/2 + 1/2))
B = 1 + 1/(2 + 1/(5/2))  or on a dit que 1/(5/2) = 2/5 donc
B = 1 + 1/(2 + 2/5)
B = 1 + 1/(2*5/5 + 2/5)
B = 1 + 1/(10/5 + 2/5)
B = 1 + 1/(12/5) ici on a 1 / (12/5) = 5/12 donc
B = 1 + 5/12
B = 12/12 + 5/12
B = 17/12

C = 1 + 1/(2 + 1/(2 + 1/(2 + 1/2)))
C = 1 + 1/(2 + 1/(2 + 1/(4/2 + 1/2)))
C = 1 + 1/(2 + 1/(2 + 1/(5/2)))
C = 1 + 1/(2 + 1/(2 + 2/5))
C = 1 + 1/(2 + 1/(10/5 + 2/5))
C = 1 + 1/(2 + 1/(12/5))
C = 1 + 1/(2 + 5/12)
C = 1 + 1/(2*12/12 + 5/12)
C = 1 + 1/(24/12+5/12)
C = 1 + 1/(29/12)
C = 1 + 12/29
C = 29/29 + 12/29
C = 41/29

b) A = 7/5
A = 1,400000

B = 17/12
B = 1,416667

C = 41/29
C = 1,413793

c) V2 se lit racine de 2
V2 = 1,414214

d) V2-A = V2-7/5 = 1,414214 - 1,400000 = 0,014214
V2-B = V2-17/12 = 1,414214 - 1,416667 = -0,002453
V2-C = V2-41/29 = 1.414214 - 1.413793 = 0,000421

Merci beaucoup vous etes tres compétente en explication et miracle j'ai tout compris
Merci à toi :)