For Which Positive Integers K Is the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( k n ! ) }$

question 156

Multiple Choice

For which positive integers k is the series $\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( k n ! ) }$ convergent?

• A) \(k \geq 4\)
• B) \(k \leq - 4\)
• C) \(k \leq 0\)
• D) \(k \geq 0\)
• E) \(k \geq 1\)

---

Definitions:

Correct Punctuation

The accurate use of symbols in writing that clarifies meaning and separates structural or logical elements of text.

Incorrect Citation

The inaccurate or erroneous referencing of sources in academic or professional writing, which can undermine the credibility of the work.

Logic Problem

A puzzle or challenge that requires the use of reasoning and critical thinking skills to solve.

Idea Incomplete

A concept or thought that has not been fully developed or lacks necessary details.