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:

Coercive Power

The power to force someone to do something by threatening, punishing, or using other forms of pressure.

Legitimate Power

The power a person receives as a result of their position in the formal hierarchy of an organization.

Referent Power

A form of influence based on the charisma and interpersonal appeal of the power-holder, rather than on formal positions or commands.

Virtuous Power

Power exercised with moral integrity and for the greater good, often characterized by fairness, justice, and a concern for others' well-being.