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:

Job Satisfaction

The degree of pleasure an individual derives from their job, impacting their motivation and performance.

Scientific-Management

A management theory that analyzes and synthesizes workflows, aiming to improve economic efficiency, especially labor productivity, by scientific methods.

Theory X

A management concept proposed by McGregor suggesting that employees are inherently lazy and need constant supervision and control to be productive.

Human-Relations Approach

A management theory focusing on the importance of interpersonal relationships and motivation for enhancing worker productivity.