Question

O valor da soma 2x/3 + 4x/9 + 8x/27 + 16x/81 + ... = 10 é igual a:
A) 5
B) 10
C) 12
D) 15
E) 200/3

Answer 1

2x/3 + 4x/9 + 8x/27 + 16x/81 + ... = 10

x*(2/3 + 4/9 + 8x/27 + 16/81 + ... )= 10

q=(4/9)/(2/3)=2/3       ...Sn=a1/(1-q)   .....-1<q<1

Sn=(2/3)/(1- 2/3)=(2/3)/(1/3) = 2

x*2= 10

x=5