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:  $\dfrac{5}{4}$

Step-by-step explanation:

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

The seconds term of Geometric series : $ar=\dfrac{1}{5}$

The common ratio between the terms is given by :-

$r=\dfrac{ar}{a}=\dfrac{\frac{1}{5}}{1}=\dfrac{1}{5}$

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

$S_{\infty}=\dfrac{a}{1-r}\\\\\Rightarrow\ S_{\infty}=\dfrac{1}{1-\frac{1}{5}}=\dfrac{1}{\frac{4}{5}}\\\\\Rightarrow\ S_{\infty}=\dfrac{5}{4}$

Hence, the sum of the given infinite series = $\dfrac{5}{4}$