The Terms of a Series Are Defined Recursively by the Equations

question 5

Short Answer

The terms of a series are defined recursively by the equations $a _ { 1 } = 6 , a _ { n + 1 } = \frac { 7 n + 1 } { 6 n + 3 } a _ { n }$ .
Determine whether $\sum a _ { n }$ converges or diverges.

---

Definitions:

Overconfidence And Egocentrism

The tendency to overestimate one's abilities or knowledge, often accompanied by a lack of empathy or consideration for others' perspectives.

Physical Appearance

Refers to the observable physical traits of an individual, including body shape, facial features, hair, and style, which can significantly influence both self-perception and social interactions.

Emotional Immaturity

A state characterized by a lack of emotional development, which impacts an individual's relationships and coping mechanisms.

Social Status

The relative position or rank of a person within a society or social group, often determined by wealth, occupation, or other social norms.