Question

halla la suma de los 13 terminos de la progresion geometrica 1/9,1/3,1,3,9 ...

Answer 1

Tenemos.

a₁ = Primer termino  = 1/9
r = Razon = 1/3 ÷ 1/9 = 1/3 . 9/1 = 9/3 = 3
an = Ultimo termino
n = Número de terminos = 13


Formula.
an = a₁ . rⁿ⁻¹
an = 1/9 . 3¹³⁻¹
an = 1/9 . 3¹²
an = 1/9 *
an = 1/9 * 531441
an = 531441/9
an = 59049

Suma de los terminos.

S = (an . r - a₁)/(r- 1)
S = (59049 * 3 - 1/9)/(3- 1)
S = (117147 - 1/9)/2
S = (1594323/9 - 1/9)/ 2
S = [(1594323 - 1)/9]/2
S = [(1594322)/9)]/2
S = 1594322/18
S = 88573,444

Respuesta.
La suma de los 13 terminos es 88573.444 aproximadamente