Question

Se x/2 + x/6 + x/18+...=1-x então x é igual a:
a)3/7
b)4/7
C)3/4
d)4/3
e)3/2

Answer 1

a1 = x/2
a2 = x/6
a3 = x/18 
q = x/6 : x/2 = x/6 * 2/x  = 2x/6x = 2/6 = 1/3 ***

Sn = 1 - x
Sn =  a1/ ( 1 - q)
1 - x =(x/2)  / ( 1 - 1/3)
(1 - x)/1  = ( x/2 ) / ( 2/3)
x/2 =  2/3( 1 - x)
x/2 = ( 2 - 2x)/3
3x = 2 ( 2 - 2x)
3x = 4 - 4x
3x + 4x =  4
7x = 4
x = 4/7 ***  ( B )
a1 = x/2 =  4/7 : 2/1 = 4/7 * 1/2 = 4/14 = 2/7**
a2 = x/6 = 4/7 : 6/1 = 4/7 * 1/6 = 4/42 = 2/21***
a3 = x/18 = 4/7 : 18/1 =4/7 * 1/18 = 4/126 = 2/63***