Use the Principle of Mathematical Induction to Prove That $$1 + 4 + 7 + 10 + \cdots + ( 3 n - 2 ) = \frac { n ( 3 n - 1 ) } { 2 } \text { for all }$$

question 6

Short Answer

Use the Principle of Mathematical Induction to prove that $$1 + 4 + 7 + 10 + \cdots + ( 3 n - 2 ) = \frac { n ( 3 n - 1 ) } { 2 } \text { for all }$$ n ≥ 1.

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Definitions:

Separation Anxiety

A disorder characterized by excessive fear or anxiety about separation from home or an attachment figure.

Assimilation

A cognitive process in which new information is integrated into existing schemas or frameworks in the mind.

Jean Piaget

A Swiss developmental psychologist best known for his theory of cognitive development that describes how children develop intellectual abilities from infancy to adolescence.

Sensorimotor Stage

The first of the four stages of cognitive development in Piaget's theory, occurring from birth to about 2 years of age, where infants learn about the world through their movements and sensory experiences.