Find the Sum of the Geometric Series for Those X $$\sum _ { n = 0 } ^ { \infty } ( 9 x + 1 ) ^ { n }$$

question 248

Multiple Choice

Find the sum of the geometric series for those x for which the series converges.
- $$\sum _ { n = 0 } ^ { \infty } ( 9 x + 1 ) ^ { n }$$

• A) \(\frac { 1 } { 9 x }\)
• B) \(- \frac { 1 } { 9 x }\)
• C) \(\frac { 1 } { 1 - 9 x }\)
• D) \(\frac { 1 } { 1 + 9 x }\)

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Definitions:

Autonomous Consumption

The level of consumption that occurs when income levels are zero, representing the expenditures that consumers must make even when they have no income.

Terrible Depression

An extremely severe and prolonged downturn in economic activity, characterized by significant declines in GDP, employment, and production.

APC

Average Propensity to Consume, indicating the percentage of income that an individual or average consumer spends rather than saves.

Disposable Income

The total amount of money available for an individual or household to spend or save after taxes have been deducted.