Question

The sum of an infinite geometric series whose first term is a and common ratio is r is given by

• A. $S_{\infty }=\frac{1}{a-r}$
• B. $S_{\infty }=\frac{1}{r-a}$
• C. $S_{\infty }=\frac{a}{1-r}$
• D. $S_{\infty }=\frac{1-r}{a}$

Answer 1

Answer: (C)

$S_{\infty }=\frac{a}{1-r}$

Lets say the sum of infinite geometric series is:

$S_{\infty }=a+ar+a{r}^2+a{r}^3......a{r}^n.....\infty$

Let us multiply r on both sides

$r{S}_{\infty }=ar+a{r}^2+.................\infty$

Let us subtract $r{S}_{\infty }$ to from $S_{\infty }$

So we can write

$S_{\infty }-r{S}_{\infty }=a$

$S_{\infty }(1-r)=a$

$S_{\infty }=\frac{a}{1-r}$