Use Mathematical Induction to Prove That the Statement Is True

question 56

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$5 + 5 \cdot \frac { 1 } { 5 } + 5 \cdot \left( \frac { 1 } { 5 } \right) ^ { 2 } + \ldots + 5 \cdot \left( \frac { 1 } { 5 } \right) ^ { n - 1 } = \frac { 5 \left( 1 - \left( \frac { 1 } { 5 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 5 } }$$

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Definitions:

Total Productivity

The ratio of total output (goods and services) produced to the total inputs used to obtain that output, measuring efficiency in production.

Union Labor

Workforce that is organized in trade unions which negotiate wages, working conditions, and benefits on their behalf.

Production Process

The production process involves the steps, operations, and methodologies utilized to transform raw materials and components into finished goods or services.

Market Conditions

The various factors that influence the supply and demand of goods and services, including prices, competition, and overall economic climate.