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:

Formation

The process of being formed or coming into being; in geology, it refers to a body of rock with a particular set of characteristics.

Reaction

A procedure where substances combine, leading to the creation of new substances.

Yield

The amount of product produced in a chemical reaction, typically expressed as a percentage of the theoretical maximum based on the reactants used.

Carbonyl

A functional group consisting of a carbon atom double-bonded to an oxygen atom, found in aldehydes, ketones, carboxylic acids, and their derivatives.