Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } } { 3 ( n + 1 ) ( n + 2 ) }$

question 90

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } \frac { n ^ { 2 } } { 3 ( n + 1 ) ( n + 2 ) }$ is convergent or divergent. If it is convergent, find its sum.

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Definitions:

Equilibrium

A state of balance or stability within a system, where competing forces or influences are in equal opposition.

Sound Waves

Vibrations that travel through air or another medium and can be heard when they reach a person's or animal's ear.

Otolith

Small calcified structures found in the inner ear of vertebrates, crucial for balance and hearing by detecting motion and orientation.

Middle Ear

A part of the ear that contains three small bones known as the ossicles, responsible for transmitting sound from the outer ear to the inner ear.