Use the Principle of Mathematical Induction to Show That the Statement

question 57

Essay

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
- $$\frac { 1 } { 2 } + \frac { 1 } { 4 } + \frac { 1 } { 8 } + \frac { 1 } { 16 } + \ldots + \frac { 1 } { 2 ^ { n } } = 1 - \frac { 1 } { 2 ^ { n } }$$

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Definitions:

Digestive Tracts

The series of hollow organs joined in a long, twisting tube from the mouth to the anus, where food is broken down and nutrients are absorbed.

Pulp Cavity

The central part of a tooth containing the nerve and blood vessels, vital for the tooth's nutrition and sensitivity.

Tooth Decay

A condition where the structure of the tooth is damaged due to bacterial activity, leading to cavities or caries.

Dentin

The hard, dense, bony tissue that forms the bulk of a tooth beneath the enamel, providing its primary structure.