Find the Radius of Convergence Of $\sum _ { n = 1 } ^ { \infty } \frac { n ! x ^ { n } } { n ^ { n } }$

question 183

Multiple Choice

Find the radius of convergence of $\sum _ { n = 1 } ^ { \infty } \frac { n ! x ^ { n } } { n ^ { n } }$ .

• A)0
• B) \(\infty\)
• C)1/e
• D) \(\frac { 1 } { 2 }\)
• E)1
• F)e
• G)2
• H)3

---

Definitions:

Technical Analyst

A professional who evaluates securities by analyzing statistics generated from trading activity, such as price and volume.

Mental Accounting

A psychological phenomenon where people treat money differently depending on its origin, intended use, or other subjective criteria.

Gold Futures

Contracts to buy or sell gold at a future date at a price that is agreed upon today, used for speculation or hedging.

Conservatism

In finance, it refers to a risk-averse approach to investing or managing assets, prioritizing safety and preservation of capital.