Find the Indicated Partial Sum of the Series $$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$$

question 23

Multiple Choice

Find the indicated partial sum of the series. $$\sum _ { i = 1 } ^ { \infty } 2 \left( \frac { 1 } { 3 } \right) ^ { i }$$ fourth partial sum

• A) \[\frac { 2 } { 81 }\]
• B) \[\frac { 242 } { 81 }\]
• C) \(\frac { 80 } { 81 }\) ​
• D) \(\frac { 26 } { 81 }\) ​
• E) \(\frac { 82 } { 81 }\)

---

Definitions:

Companionate Love

A form of love characterized by deep affection, friendship, and emotional intimacy, often found in long-term relationships.

Passionate Love

Passionate Love is a state of intense longing for union with another, characterized by a high degree of physical arousal and emotional investment.

Transition

Describes the process or period of changing from one state or condition to another in various contexts such as social, physical, or emotional.

Sternberg's Triangular

A theory of love proposed by psychologist Robert Sternberg, which suggests three components: intimacy, passion, and commitment.