Use Mathematical Induction to Prove That the Sum of a Partial

question 74

Essay

Use mathematical induction to prove that the sum of a partial geometric sequence is $\frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$ .

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Definitions:

Tuberculosis

An infectious disease caused by the bacterium Mycobacterium tuberculosis, mainly affecting the lungs but can spread to other organs.

Pulmonary Fibrosis

Respiratory condition characterized by the buildup of connective tissue in the lungs; typically caused by inhalation of coal dust, silica, or asbestos.

Encapsulated Bacteria

Bacteria surrounded by a protective outer layer that helps them evade the immune system.

Lung Disease

A broad term for various conditions that impair lung function, including chronic obstructive pulmonary disease (COPD), asthma, and lung cancer.