Use Mathematical Induction to Prove the Statement Is True for All

question 30

Essay

Use mathematical induction to prove the statement is true for all positive integers n.
- $$5 \cdot 7 + 6 \cdot 8 + 7 \cdot 9 + \ldots + 5 n ( 5 n + 2 ) = \frac { 5 n ( 5 n + 1 ) ( 10 n + 7 ) } { 6 }$$

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Definitions:

Feelings Generated

The emotions or sensations produced in response to stimuli or experiences.

Cognitive Dissonance

A psychological state of having inconsistent thoughts, beliefs, or attitudes, especially relating to behavioral decisions and attitude changes.

Sense of Consistency

The drive or need for individuals to ensure their beliefs, attitudes, and behaviors are coherent and aligned to avoid cognitive dissonance.

Psychological Price

Pricing strategy that leverages consumer psychology, often using pricing just below a whole number (e.g., $1.99) to increase appeal.