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

question 205

Essay

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

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Definitions:

Water Supply

The provision of water by public utilities, commercial organisations, community endeavors, or individuals, usually through a system of pumps, pipes, and treatments, for various uses including drinking, agriculture, and industry.

Freshwater

refers to water with minimal salt content, crucial for drinking, agriculture, sanitation, and ecosystem support.

Human Use

The application or utilization of resources, products, or services to satisfy human needs or wants.

Global Basis

A perspective or action at the worldwide level, considering global impact rather than local or national alone.