The series for summation is,
[tex]-\frac{4}{5},\frac{16}{26},-\frac{64}{125},\ldots[/tex]
The series is a geometric progression with a = -4/5 and r = -4/5.
The sum of infinite terms of a GP is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]
Substitute the values in the sum formula to obtain the sum of infinite terms of a GP.
[tex]\begin{gathered} S_{\infty}=\frac{-\frac{4}{5}}{1-(-\frac{4}{5})} \\ =\frac{-4}{5\cdot(1+\frac{4}{5})} \\ =-\frac{4}{5}\cdot\frac{5}{9} \\ =-\frac{4}{9} \end{gathered}[/tex]
Answer: -4/9
