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 $c _ { n }$ .

---

Definitions:

Criminal Vicarious Liability Doctrine

A legal principle holding one person or entity responsible for the criminal actions of another, typically in an employer-employee relationship.

Corporate Criminal Doctrine

A legal theory that attributes criminal liability to corporations and their executives for acts that are illegal under the law, acknowledging that entities can be responsible for criminal behavior.

Deadly Force

Force that is likely to cause death or serious bodily harm, often discussed in the context of law enforcement or self-defense.

Provide a Defense

To offer arguments or evidence in support of oneself in legal proceedings or when accused of something.