Respuesta :
Answer:
Option B is correct.
Step-by-step explanation:
Given Geometric series : 3 , 1 , [tex]\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}[/tex]
To find: Sum of the series.
First term of the geometric series, a = 3
Common ration of the Geometric series, r = [tex]\frac{second\:term}{first\:term}=\frac{1}{3}[/tex]
Sum of the finite Geometric series , [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Sum of the given 5 term term of given series , [tex]S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}[/tex]
= [tex]\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}[/tex]
Therefore, Option B is correct.
