Use Mathematical Induction to Prove That the Statement Is True $$5 + 2 \cdot 5 + 3 \cdot 5 + \ldots + 5 n = \frac { 5 n ( n + 1 ) } { 2 }$$

question 224

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$5 + 2 \cdot 5 + 3 \cdot 5 + \ldots + 5 n = \frac { 5 n ( n + 1 ) } { 2 }$$

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Definitions:

Different Sense

The ability to interpret and distinguish diverse types of sensory information, such as visual, auditory, and tactile stimuli.

Impulsive

Impulsive pertains to actions or behaviors initiated without forethought or consideration of the consequences.

Ventromedial Prefrontal Cortex

A region of the frontal lobe in the brain implicated in the processing of risk and fear, decision-making, and the regulation of emotions.

Nucleus Accumbens

A region in the brain associated with the reward circuit, critical in processing rewards, motivation, pleasure, and reinforcement learning.