Verified answer

Réponse :

Bonsoir

Explications étape par étape

U0 = 5 et q = 1/2

Un+1 = q x U0

U1 = 1/2 x 5 = 5/2

U2 = 1/2 x 5/2 = 5/4

U3 = 5/8

U4 = 5/16

U5 = 5/32

U6 = 5/64

U7 = 5/128

U8 = 5/256

U9 = 5/512

U10 = 5/1024

U11 = 5/2048

U12 = 5/4096

U13 = 5/8192

Somme :

5/32 + 5/64 + 5/128 + 5/256 + 5/512 + 5/1024 + 5/2048 + 5/4096 + 5/8192 =

1280/8192 + 640/8192 + 320/8192 + 160/8192 + 80/8192 + 40/8192 + 20/8192 + 10/8192 + 5/8192 =

2555/8192 ~ 0,312

Somme = U5 x [1 - (1/2)^12] / (1/2)