Find the Sum of the Geometric Series for Those X $$\sum _ { \mathrm { n } = 0 } ^ { \infty } \left( \frac { \mathrm { x } - 2 } { 7 } \right) ^ { \mathrm { n } }$$

question 118

Multiple Choice

Find the sum of the geometric series for those x for which the series converges.
- $$\sum _ { \mathrm { n } = 0 } ^ { \infty } \left( \frac { \mathrm { x } - 2 } { 7 } \right) ^ { \mathrm { n } }$$

• A) \(\frac { 2 } { 9 + x }\)
• B) \(\frac { 7 } { 9 - x }\)
• C) \(\frac { 7 } { 9 + x }\)
• D) \(\frac { 2 } { 9 - x }\)

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Definitions:

Consumption

The part of personal income that is spent on goods and services rather than saved, influencing economic activity and demand.

Savings

The portion of income not spent on current expenditures or taxes, which is set aside for future use or investment.

Autonomous Consumption

Spending that does not depend on current income levels, such as basic necessities, implying that this consumption occurs even in the absence of income.

Disposable Income

represents the amount of money that households have available for spending and saving after income taxes have been accounted for.