Question

Resolva a equação x-1/5 - x-1/25 + x-1/125 - ...=6.

Answer 1

Boa noite

(x - 1)/5 - (x - 1)/25 + (x - 1)/125 + ... = 6

(x - 1)*(1/5 + 1/25 + 1/125 + ...) = 6 

PG infinita

u1 = 1/5
u2 = 1/25

q = u2/u1 = (1/25)/(1/5) = 1/5 

soma infinita

Sn = u1/(1 - q)
Sn = (1/5)/(1 - 1/5)
Sn = (1/5)/(4/5) = 1/4 

(x - 1)/4 = 6
x - 1 = 24
x = 25