Question

Number 19question: find the sum of each infinite geometric serie please help

Answer 1

Answer:

The sum of the given geometric series is 16/5

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula:

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

where a is the first term and r is the common ratio.

`\begin{gathered} r=((-(4)/(5)))/(((8)/(5)))=-(4)/(5)*(5)/(8)=(4)/(8)=(1)/(2) \\ \\ a=(8)/(5) \end{gathered}`

Using these, we have:

`\begin{gathered} S_(\infty)=(((8)/(5)))/(1-((1)/(2))) \\ \\ =(((8)/(5)))/((1)/(2)) \\ \\ =(8)/(5)*(2)/(1) \\ \\ =(16)/(5) \end{gathered}`