Use Mathematical Induction to Prove the Given Statement for All $$1 \cdot 4 + 2 \cdot 7 + 3 \cdot 10 + \ldots + n ( 3 n + 1 ) = n ( n + 1 ) ^ { 2 }$$

question 21

Short Answer

Use mathematical induction to prove the given statement for all positive integers n.
- $$1 \cdot 4 + 2 \cdot 7 + 3 \cdot 10 + \ldots + n ( 3 n + 1 ) = n ( n + 1 ) ^ { 2 }$$

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Definitions:

Approach-Avoidance Conflict

A psychological conflict that occurs when a single goal or event has both attractive and unattractive aspects, leading to internal struggle.

Prestige

The respect and admiration that an individual or organization gains based on their achievements or quality.

Hard Work

Persistent effort applied towards achieving a goal or completing tasks.

Avoidance-Avoidance Conflict

A situation where an individual must choose between two negative outcomes.