Which One of the Following Series Diverge?
A) $\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( 2 n + 1 ) }$

question 286

Multiple Choice

Which one of the following series diverge?

• A) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n ( 2 n + 1 ) }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { 2 n } { n + 1 }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( n + 1 ) ( n + 3 ) }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { 3 ^ { n } }\)
• E) \(\sum _ { n = 1 } ^ { \infty } \frac { n - 2 } { n 2 ^ { n } }\)
• F) \(\sum _ { n = 1 } ^ { \infty } \frac { 2 n } { n ! }\)
• G) \(\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 100 } } { n ! }\)
• H) \(\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 100 } } { 2 ^ { n } }\)

---

Definitions:

Colon

A major part of the large intestine, responsible for absorbing water and electrolytes from partially digested food and forming and storing feces.

Muscle Weakness

A decrease in the strength of one or more muscles, potentially affecting the ability to perform physical tasks.

Mobility Device

A mobility device is an apparatus designed to assist individuals with walking or otherwise improve their mobility, such as crutches, walkers, or wheelchairs.

Bedside Commode

A portable toilet, usually placed near a patient's bed, for individuals who are unable to walk to the bathroom.