Use Mathematical Induction to Prove the Given Statement for All

question 151

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$\left( 1 - \frac { 1 } { 3 } \right) \left( 1 - \frac { 1 } { 4 } \right) \left( 1 - \frac { 1 } { 5 } \right) \ldots \left( 1 - \frac { 1 } { n + 2 } \right) = \frac { 2 } { n + 2 }$$

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Definitions:

Marginal Product

The additional output gained from employing one more unit of a particular input while keeping other inputs constant.

Marginal Revenue Product

The supplementary earnings derived from utilizing an extra unit of a resource, like labor or capital.

Variable Resource

Inputs or resources used in production that change in amount with the level of output, such as labor or raw materials.

Unskilled Labor

Labor that requires no specialized skills, education, or training.