Question

1 9 = 0.1 + 0.01 + 0.001 + 0.0001 + … representa un proceso

Answer 1

Respuesta:

S∞ = 1 / 9

Explicación:

1 / 9 = 0.1 + 0.01 + 0.001 + 0.0001 + …

a1 = 0.1 , a2 = 0.01

Razón: r

r = a2 / a1 = 0.01 / 0.1 = 0.1

r = 0.1 = 1 / 10

Suma infinita:

S∞ = a1 / 1 - r  ; r ≠ 1.

S∞ = 0.1 / 1 - 0.1 = 0.1 / 0.9 = (1/10) / (9/10) = 1 / 9

S∞ = 1 / 9