Question

An infinite geometric series has 1 and 1/5 as its first two terms: 1, 1/5, 1/25, 1/125, . . . What is the sum, S, of the infinite series? A. 1 B. 5/4 C. 1/4 D. 1/25

Answer 1

Answer:
`(5)/(4)`

Explanation:

Given: The first term of Geometric series : a=1

The seconds term of Geometric series :
`ar=(1)/(5)`

The common ratio between the terms is given by :-

`r=(ar)/(a)=((1)/(5))/(1)=(1)/(5)`

We know that the sum of infinite geometric series is given by :-

`S_(\infty)=(a)/(1-r)\\\\\Rightarrow\ S_(\infty)=(1)/(1-(1)/(5))=(1)/((4)/(5))\\\\\Rightarrow\ S_(\infty)=(5)/(4)`

Hence, the sum of the given infinite series =
`(5)/(4)`