Determine Whether the Sequence Defined By $a _ { n } = \frac { n ^ { 2 } - 5 } { 6 n ^ { 2 } + 1 }$

question 15

Multiple Choice

Determine whether the sequence defined by $a _ { n } = \frac { n ^ { 2 } - 5 } { 6 n ^ { 2 } + 1 }$ converges or diverges. If it converges, find its limit.

• A) \(\frac { 1 } { 6 }\)
• B) \(- 5\)
• C) \(- \frac { 5 } { 6 }\)
• D) Diverges

---

Definitions:

Autonomous Thinking

Independent thinking that is not influenced by others' opinions or beliefs; self-directed reasoning.

Heteronomous Thinking

A stage in cognitive development where children believe that rules are unchangeable and given by authority, typically associated with Jean Piaget's moral development stages.

Preconventional Moral Thought

The first stage in Kohlberg's theory of moral development, where behavior is influenced by the consequences of actions, including punishment and reward.

Immanent Justice

Piaget’s concept of the childhood expectation that if a rule is broken, punishment will be meted out immediately.