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Write the Word or Phrase That Best Completes Each Statement 3+34+316++34n1=4(114n)3 + \frac { 3 } { 4 } + \frac { 3 } { 16 } + \ldots + \frac { 3 } { 4 ^ { n - 1 } } = 4 \left( 1 - \frac { 1 } { 4 ^ { n } } \right)

question 258

Essay

Write the word or phrase that best completes each statement or answers the question. Use mathematical induction to prove that the statement is true for every positive integer n.
- 3+34+316++34n1=4(114n)3 + \frac { 3 } { 4 } + \frac { 3 } { 16 } + \ldots + \frac { 3 } { 4 ^ { n - 1 } } = 4 \left( 1 - \frac { 1 } { 4 ^ { n } } \right)


Definitions:

United States

A country located primarily in North America, consisting of 50 states and a federal district.

Hats

A headwear item designed for various purposes including protection from weather, ceremonial reasons, religious reasons, safety, or fashion.

Production

The method of integrating different physical and non-physical inputs, such as materials and ideas, to produce goods for use.

Opportunity Costs

Missing out on potential benefits from various options due to the selection of a single alternative.

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