What is the sum of the geometric series below?
3+1+1/3+1/9+1/27
answer is b. 121/27
3+1+1/3+1/9+1/27
= 3+1+9/27+3/27+1/27
= 4 13/27
= 121/27
Answer:
Option B is correct.
Step-by-step explanation:
Given Geometric series : 3 , 1 , \(\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}\)
To find: Sum of the series.
First term of the geometric series, a = 3
Common ration of the Geometric series, r = \(\frac{second\:term}{first\:term}=\frac{1}{3}\)
Sum of the finite Geometric series , \(S_n=\frac{a(1-r^n)}{1-r}\)
Sum of the given 5 term term of given series , \(S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}\)
= \(\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}\)
Therefore, Option B is correct.