Determine whether the geometric series converges or diverges.If it converges, find its sum. 
Definitions:
Federico Fellini
An iconic Italian film director and screenwriter known for his distinctive style that blends fantasy and baroque images with earthiness.
Ingmar Bergman
A renowned Swedish director and writer known for his deeply personal and introspective films.
Hollywood Renaissance
A period in the late 1960s and early 1970s marked by a significant shift in American cinema, characterized by the production of more sophisticated and artistic films.
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The depiction of extreme acts of violence within the horror film genre, often used to elicit fear, disgust, or shock from the audience.
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