Question

determine a soma da pg infinita (1/3+2/9+2/27+...)

Answer 1

Bom dia 

PG

1/3 + 2*PG( 1/9 + 1/27 +1/81...)

u1 = 1/9
u2 = 1/27
u3 = 1/81

razâo
q = u2/u1 = (1/27)/(1/9) = 1/3 

soma infinita
Sn = u1/(1 - q)
Sn = (1/9)/(1 - 1/3)
Sn = (1/9)/(2/3) = (1/9)*(3/2) = 1/6  

S = 1/3 + 2*(1/6) = 1/3 + 1/3 = 2/3