Question

The infinite geometric series S=1+( 2/3 )+( 2/3 )^ 2 +( 2/3 )^ 3 .... equal to:

Answer 1

SOLUTION

The question simply means that we should find the sum to infinity of the geometric series.

The formula of sum to infinity of a geometric serie is given by

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

Where

$\begin{gathered} S_{\infty}\text{ is the sum to infinity} \\ \\ a\text{ is the first term = 1} \\ \\ r\text{ is the common ratio = }\frac{2}{3} \end{gathered}$

So, this becomes

$\begin{gathered} S_{\infty}=\frac{a}{1-r} \\ \\ S_{\infty}=\frac{1}{1-\frac{2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{3-2}{3}} \\ \\ S_{\infty}=\frac{1}{\frac{1}{3}} \\ \\ S_{\infty}=3 \end{gathered}$

Therefore, option b is the correct answer