Determine Whether the Sequence $\alpha _ { n } = \frac { 1 } { e ^ { n } }$

question 58

Essay

Determine whether the sequence $\alpha _ { n } = \frac { 1 } { e ^ { n } }$ converges or diverges. If it converges, find the limit.

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Definitions:

Guaiac Test

A diagnostic screening tool used to detect the presence of occult (hidden) blood in stool, an indicator of various gastrointestinal disorders.

Gastrointestinal Bleeding

The loss of blood occurring within the gastrointestinal tract, which can manifest as vomit or stool appearing black or bloody.

Menstruating

The process of shedding the uterine lining, resulting in bleeding through the vagina, which typically occurs as part of the monthly menstrual cycle in human females.

Gastroenterology

A branch of medicine focused on the digestive system and its disorders.