Determine Whether the Given Geometric Series Converges,and If So,find Its $\sum _ { n = 1 } ^ { \infty } \left( - \frac { 5 } { 9 } \right) ^ { n }$

question 7

Multiple Choice

Determine whether the given geometric series converges,and if so,find its sum. $\sum _ { n = 1 } ^ { \infty } \left( - \frac { 5 } { 9 } \right) ^ { n }$

• A)Converges to \(- \frac { 5 } { 14 }\)
• B)Converges to \(\frac { 5 } { 4 }\)
• C)Diverges
• D)Converges to \(\frac { 9 } { 14 }\)

---

Definitions:

Dollar Sales

The complete income derived from the sale of products or services, measured in units of currency.

Break-even

The point at which total costs and total revenue are equal, resulting in no net loss or gain, and where the business covers all its costs with its sales revenue.

Monthly Dollar Sales

The total value of sales measured in dollars that a business achieves in one month.

Break-even Point

A situation where the total earnings are equivalent to the total costs, therefore no profit or loss is made.