Find the Limit of the Sequence If It Converges; Otherwise $$a _ { n } = \sqrt [ n ] { 5 ^ { n } \cdot n }$$

question 16

Multiple Choice

Find the limit of the sequence if it converges; otherwise indicate divergence.
- $$a _ { n } = \sqrt [ n ] { 5 ^ { n } \cdot n }$$

• A) 1
• B) 5
• C) 0
• D) Diverges

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Definitions:

Sequence

An ordered list or arrangement where items are consecutively positioned based on certain criteria.

Modus Ponens

A form of logical argument where a premise, if true, inevitably leads to a particular conclusion.

Modus Tollens

A logical argument form where if the consequent is not true, then the antecedent cannot be true; often formatted as "If P, then Q. Not Q, therefore not P."

Deductive Reasoning

A rational procedure where an outcome is derived from the agreement of several statements, which are widely accepted as true.