Determine Whether the Sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 5 } { 4 n ^ { 4 } } \left[ \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } \right]$

question 33

Essay

Determine whether the sequence $a _ { n } = \lim _ { n \rightarrow \infty } \frac { 5 } { 4 n ^ { 4 } } \left[ \frac { n ^ { 2 } ( n + 1 ) ^ { 2 } } { 4 } \right]$ converges or diverges. If it converges, find the limit.

---

Definitions:

Raw Materials

Basic materials and components required in the manufacturing process to produce finished goods.

Direct Labor

Costs associated with employees who directly manufacture or produce goods, such as wages for factory workers.

Overhead

Refers to the ongoing business expenses not directly attributed to creating a product or service, such as rent, utilities, and administrative costs.

Work In Process Inventory

Work In Process Inventory consists of partially completed goods that are still in production, representing a component of a manufacturing company's inventory.