Use Mathematical Induction to Prove the Statement Is True for All

question 41

Essay

Use mathematical induction to prove the statement is true for all positive integers n.
- $$1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

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Definitions:

Industrial Policy

Governmental strategies aimed at encouraging development and growth in the industrial sector of an economy through a mix of policies including subsidies, tax incentives, and investments in infrastructure and innovation.

Government Policy

The set of laws and regulations enacted by government officials that affect the operations of a country or region.

Competitiveness

The ability of a company, sector, or country to produce goods or services that meet the test of international markets while maintaining or increasing the real incomes of its citizens.

Critics Of Industrial Policy

Critics of industrial policy argue that government efforts to direct and support specific industries often lead to inefficiency, corruption, and a misallocation of resources.