The sum to infnity of the series is;
[tex]S\infty\text{ = 1,066}\frac{2}{3}[/tex]
Here, we want to find the sum to infinity of the given geometric series
We have this as follows;
[tex]S_{\infty}\text{ =}\frac{a}{1-r}[/tex]
a is the first term which is 800
The common ratio is r and it is the second term divided over the first or the third over the second
We have this as;
[tex]\frac{200}{800}\text{ = }\frac{50}{200}\text{ = }\frac{1}{4}\text{ =0.25}[/tex]
Substituting these values, we have it that;
[tex]S_{\infty}\text{ = }\frac{800}{1-0.25}\text{ = }\frac{800}{0.75}\text{ = 1,066 }\frac{2}{3}[/tex]
