Find the Sum of the Infinite Geometric Series $a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldots$

question 61

Essay

Find the sum of the infinite geometric series. $a + a x ^ { 2 } + a x ^ { 4 } + a x ^ { 6 } + \ldots$

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Definitions:

Psychological Test

A standardized measure of a sample of a person’s behavior, used to assess and evaluate diverse mental functions and characteristics.

Mental Status Examination

The most frequently used semi-structured interview in psychiatric settings. Screens for patients’ emotional, intellectual, and neurological functioning. Used in formal diagnosis or to plan treatment.

Sensorium

The total sensory apparatus of the body, including the perception and processing of sensory information.

Detect Sarcasm

The ability to interpret and understand sarcasm, often through recognizing tone, context, or social cues that imply a discrepancy between the literal and intended meaning.