Find the Sum of the Infinite Geometric Series $\frac { 1 } { 3 } + \frac { 2 } {9 } + \frac { 4 } { 27 } + \frac { 8 } { 81 } + \cdots$

question 57

Essay

Find the sum of the infinite geometric series $\frac { 1 } { 3 } + \frac { 2 } {9 } + \frac { 4 } { 27 } + \frac { 8 } { 81 } + \cdots$ .

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Definitions:

Relationship

A connection, association, or involvement between individuals or entities based on emotions, commitments, or agreements.

Dishwasher

A mechanical device used for cleaning dishes and cutlery automatically, significantly reducing manual labor in kitchen cleaning tasks.

ABC Model

A framework used in psychology, particularly in cognitive-behavioral therapy, that describes the interrelation between affect (emotions), behavior, and cognition (thoughts).

Attitudes

A rephrased definition: Stable, learned predispositions to respond in a consistently favorable or unfavorable manner towards a given object or situation.