For Which Positive Integers $k$ Is the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 5 } } { ( k n ) ! }$

question 13

Multiple Choice

For which positive integers $k$ is the series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 5 } } { ( k n ) ! }$ convergent?

• A) \(k \geq 5\)
• B) \(k \leq 0\)
• C) \(k \geq 0\)
• D) \(k \geq 1\)
• E) \(k \leq - 5\)

---

Definitions:

Physical Assets

Tangible objects that hold value, such as real estate, machinery, vehicles, or commodities, often used in the production of goods and services.

Opportunity Cost

The value of the next best alternative forgone as a result of making a decision.

Private Ownership

The holding of property by non-governmental legal entities or individuals.

Conservation Of Resources

Involves managing natural resources wisely to prevent depletion and ensure sustainability for future generations.