Consider the Sequence Defined By $a _ { n } = ( - 1 ) ^ { n }$

question 293

Essay

Consider the sequence defined by $a _ { n } = ( - 1 ) ^ { n }$ . (n starts at 1)
(a) Write the first five terms of the sequence.(b) Determine the limit of the sequence.(c) Let $b _ { n } = \frac { a _ { n + 1 } } { a _ { n } }$ . Write the first five terms of this sequence.(d) Determine the limit of $b _ { n }$ .(e) Let $c _ { n } = \sum _ { k = 1 } ^ { n } a _ { k }$ . Write the first five terms of this sequence.(f) Determine the limit of $c _ { n }$ .

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Definitions:

Cognitive Competence

The ability to mentally process information, reason, remember, and relate objects and symbols with understanding and problem-solving skills.

Media Violence

Refers to the depiction of violent acts in media sources, such as television, movies, and video games, and its potential impact on viewers' behavior and attitudes.

Child Aggression

Manifestations of hostile or violent behavior by children towards others, which can be physical, verbal, or relational.

Circular Relationship

A connection between two or more variables where each influences the other in a continuous loop.