Determine the Sum of the Following Geometric Series $1 + ( 0.25 ) ^ { 2 } + ( 0.25 ) ^ { 4 } + ( 0.25 ) ^ { 8 } + \ldots$

question 53

Short Answer

Determine the sum of the following geometric series: $1 + ( 0.25 ) ^ { 2 } + ( 0.25 ) ^ { 4 } + ( 0.25 ) ^ { 8 } + \ldots$ .
Enter a reduced fraction of form $\frac { a } { b }$ .

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Definitions:

Acronym

A word formed from the initial letters of other words and pronounced as a single word (e.g., NATO, laser).

Big Five

A model describing five broad dimensions of human personality traits: openness, conscientiousness, extraversion, agreeableness, and neuroticism, used in psychological assessment.

Personality Traits

Enduring characteristics that describe an individual's behavior, mindset, and emotional patterns.

Serial-Position Effect

The tendency for individuals to recall the first and last items in a series best, and the middle items worst.