Suppose the annual spending by tourists in a resort city is $100 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Summing all of this spending indefinitely, leads to the geometric series $\sum _ { i = 0 } ^ { \infty } 100 \left( 0.75 ^ { i } \right)$. Find the sum of this series.
A) $\$ 800$ million
B) $\$ 401$ million
C) $\$ 200$ million
D) $\$801$ million
E) $\$ 400$ million

Question

Quizplus · Accepted Answer

The sum of an infinite geometric series is given by $ S = \frac{a}{1 - r} $, where $ a = 100 $ million and $ r = 0.75 $. Thus, $ S = \frac{100}{1 - 0.75} = \frac{100}{0.25} = 400 $ million dollars.

Suppose the Annual Spending by Tourists in a Resort City ∑i=0∞100(0.75i)\sum _ { i = 0 } ^ { \infty } 100 \left( 0.75 ^ { i } \right)∑i=0∞​100(0.75i)

Suppose the Annual Spending by Tourists in a Resort City $\sum _ { i = 0 } ^ { \infty } 100 \left( 0.75 ^ { i } \right)$