Answer:
The sum of the given geometric series is 16/5
Explanation:
The sum of an infinite geometric series is given by the formula:
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
where a is the first term and r is the common ratio.
[tex]\begin{gathered} r=\frac{(-\frac{4}{5})}{(\frac{8}{5})}=-\frac{4}{5}\times\frac{5}{8}=\frac{4}{8}=\frac{1}{2} \\ \\ a=\frac{8}{5} \end{gathered}[/tex]
Using these, we have:
[tex]\begin{gathered} S_{\infty}=\frac{(\frac{8}{5})}{1-(\frac{1}{2})} \\ \\ =\frac{(\frac{8}{5})}{\frac{1}{2}} \\ \\ =\frac{8}{5}\times\frac{2}{1} \\ \\ =\frac{16}{5} \end{gathered}[/tex]
