ANSWER
[tex]S_\infty= 686[/tex]
EXPLANATION
The given infinite series is
[tex]98 + 84 + 72 + \frac{432}{7} + ...[/tex]
The sum to infinity of this series is given by the formula,
[tex]S_\infty= \frac{a_1}{1 - r} [/tex]
where the first term of this infinite geometric series is
[tex]a_1 = 98[/tex]
and the common ratio is
[tex]r = \frac{a_2}{a_1} [/tex]
[tex]r = \frac{72}{98} = \frac{6}{7} [/tex]
We substitute these values to obtain,
[tex]S_\infty= \frac{98}{1 - \frac{6}{7} } [/tex]
We simplify the denominator to get,
[tex]S_\infty= \frac{98}{\frac{1}{7} } [/tex]
This simplifies to
[tex]S_\infty= 98 \times 7 = 686[/tex]
