Question

find the sum of the infinite geometric series
$500 + 100 + 20 + \dots$

select one:
a. $625$
b. sum does not exist.
c. $-125$
d. $416.67$

Explanation:

Step1: Identify first term $a$

$a = 500$

Step2: Calculate common ratio $r$

$r = \frac{100}{500} = 0.2$

Step3: Verify $|r| < 1$

$|0.2| = 0.2 < 1$, sum exists.

Step4: Apply infinite sum formula

$$S = \frac{a}{1 - r}$$
$$S = \frac{500}{1 - 0.2}$$

Step5: Compute the final value

$$S = \frac{500}{0.8} = 625$$

Answer:

A. 625