Write the Word or Phrase That Best Completes Each Statement $$1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + n ( n + 1 ) = \frac { n ( n + 1 ) ( n + 2 ) } { 3 }$$

question 27

Essay

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers 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:

Profit-maximizing

The method firms apply to identify the most beneficial pricing and production levels for profit maximization.

Demand

An economic principle referring to the quantity of a good or service that consumers are willing and able to purchase at various prices during a given time period.

Inverse Demand Curve

A graphical representation that shows the relationship between the price of a good and the quantity demanded, plotted with price on the vertical axis and quantity on the horizontal.

Marginal Costs

Marginal costs represent the change in total production cost that arises when the quantity produced is incremented by one unit.