Use Mathematical Induction to Prove That the Statement Is True

question 311

Essay

Use mathematical induction to prove that the statement is true for every positive integer n.
- $$4 + 4 \cdot \frac { 1 } { 8 } + 4 \cdot \left( \frac { 1 } { 8 } \right) ^ { 2 } + \ldots + 4 \cdot \left( \frac { 1 } { 8 } \right) ^ { n - 1 } = \frac { 4 \left( 1 - \left( \frac { 1 } { 8 } \right) ^ { n } \right) } { 1 - \frac { 1 } { 8 } }$$

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Definitions:

Shrink

To decrease in size, amount, or value.

Visceral Fat

A type of body fat that is stored within the abdominal cavity and is associated with numerous health risks, including cardiovascular disease.

Internal Storage Fat

Fat located deep within the body, surrounding organs and providing cushioning, insulation, and energy storage.

Muscle Mass

Refers to the total amount of muscle tissue in the body, important for posture, movement, and overall metabolic rate.