Question

Calculate the sum of the infinite series 98+84+72+432/7+...

Answer 1

ANSWER

$S_\infty= 686$


EXPLANATION

The given infinite series is

$98 + 84 + 72 + \frac{432}{7} + ...$

The sum to infinity of this series is given by the formula,

$S_\infty= \frac{a_1}{1 - r}$

where the first term of this infinite geometric series is

$a_1 = 98$


and the common ratio is
$r = \frac{a_2}{a_1}$


$r = \frac{72}{98} = \frac{6}{7}$


We substitute these values to obtain,


$S_\infty= \frac{98}{1 - \frac{6}{7} }$

We simplify the denominator to get,


$S_\infty= \frac{98}{\frac{1}{7} }$


This simplifies to

$S_\infty= 98 \times 7 = 686$

Answer 2

Answer:

D. 686

Step-by-step explanation: