A Sequence Is Defined By $a _ { n } = 0.9999 ^ { n }$

question 128

Essay

A sequence is defined by $a _ { n } = 0.9999 ^ { n }$ .(a) Calculate $a _ { 10 ^ { 3 } }$ and $a _ { 10 ^ { 5 } }$ .(b) Determine whether $a _ { n }$ converges or diverges. If it converges, find the limit.

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Definitions:

Psychopathology

The study of psychological disorders, including their symptoms, etiology (causes), and treatments.

American Psychological Association

A leading scientific and professional organization representing psychology in the United States, dedicated to advancing the creation, communication, and application of psychological knowledge to benefit society and improve people's lives.

Sexual Orientation

A person's emotional, romantic, or sexual attraction to individuals of a specific gender, which can include heterosexual, homosexual, bisexual, and other orientations.

Stigma

A mark of disgrace associated with a particular circumstance, quality, or person, often leading to discrimination.