Use the Root Test to Determine If the Series Converges $$\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { n } } { \left( n ^ { n } \right) ^ { 10 } }$$

question 295

Multiple Choice

Use the Root Test to determine if the series converges or diverges.
- $$\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { n } } { \left( n ^ { n } \right) ^ { 10 } }$$

• A) Diverges
• B) Converges

---

Definitions:

Intramuscular Injection

A method of delivering medication deep into the muscles, allowing for faster absorption into the bloodstream.

Gastrointestinal Bleeding

Bleeding occurring anywhere along the gastrointestinal tract, from the mouth to the rectum, which can manifest as vomit or stool that is bloody or black.

Packed Red Blood Cells

Red blood cells that have been separated for transfusion, used to treat or prevent symptoms of anemia.

Gauge Needle

A measure of needle thickness, with higher gauge numbers indicating thinner needles commonly used for injections.