Determine Whether the Sequence $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { n . 1 }$

question 30

Essay

Determine whether the sequence $a _ { n } = \frac { ( - 1 ) ^ { n - 1 } } { n . 1 }$ converges or diverges. If it converges, find the limit.

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Definitions:

Health

A state of complete physical, mental, and social well-being, and not merely the absence of disease or infirmity.

Disease

A condition that disrupts a person’s body or mind's normal functioning, often characterized by specific symptoms and signs.

Illness

A state of poor health, often associated with disease, infection, or abnormal physical or psychological condition.

Hospitalization

The act of admitting a patient to a hospital for treatment, observation, or other healthcare needs.