Question

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

Answer 1

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)=(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 = }(2)/(3) \end{gathered}`

So, this becomes

`\begin{gathered} S_(\infty)=(a)/(1-r) \\ \\ S_(\infty)=(1)/(1-(2)/(3)) \\ \\ S_(\infty)=(1)/((3-2)/(3)) \\ \\ S_(\infty)=(1)/((1)/(3)) \\ \\ S_(\infty)=3 \end{gathered}`

Therefore, option b is the correct answer