Question

Considere as progressões geométrica infinita (1/2,1/4,1/6,1/8,1/16....) E (1/3,1/9,1/27,1/81.....).Se A e B são as respectivas somas destas progressões então o valor de A+B é:
A)2/3
B)3/2
C)4/3
D)5/3
E)7/3
Qual é a certa

Answer 1

S ∞ = a₁ / 1 - q

A

S ∞ = 1/2 / 1 - 1/2

S ∞ = 1/2 / 1/2

S ∞ = 1/2 * ( 2/1)

S ∞ =  2/2

S ∞ =  1

B

S ∞ = 1/3  / 1 - 1/3

S ∞ = 1/3  /  2/3

S ∞ = 1/3 * (  3/2)

S ∞ = 3/6

S ∞ = 1/2

A + B

=  1 + 1/2

= 2/2 + 1/2

= 3/2

Letra B.