Write the Word or Phrase That Best Completes Each Statement

question 163

Essay

Write the word or phrase that best completes each statement or answers the question.
Use mathematical induction to prove the following statement for all positive integers n.
- $$1 + \frac { 5 } { 7 } + \frac { 25 } { 49 } + \ldots + \left( \frac { 5 } { 7 } \right) ^ { n - 1 } = \frac { 7 } { 2 } \left[ 1 - \left( \frac { 5 } { 7 } \right) ^ { n } \right]$$

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Definitions:

Exclusive Contract System

Refers to a historical practice in the film industry where actors, directors, and other talent were signed under contract to a single studio, limiting their ability to work with others.

Olivia de Havilland

A British-American actress famous for her roles during the Golden Age of Hollywood, including that in "Gone with the Wind" (1939).

Typecast

The practice of casting an actor in the same kind of role repeatedly, often limiting their opportunities to display a range of acting skills.

James Cagney

An iconic American actor, remembered for his energetic performances, distinctive vocal style, and roles in classic gangster and musical films.