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) \(\frac { 2 } { 9 - x }\)

---

Definitions:

Silent Authority

A form of influence based on the perception that someone has the right to prescribe behavior due to their positional power without the need for verbal instructions.

Upward Appeals

A strategy where an individual attempts to influence a decision or gain support by appealing to higher-level superiors or citing influential or authoritative higher sources.

Exchange

The act of giving one thing and receiving another, especially of the same type or value, in return.

Personal Appeals

Requests or attempts to persuade others based on personal relationships or emotional connections rather than logical arguments.