Determine Whether the Series Is Convergent or Divergent by Expressing $S _ { n }$

question 109

Short Answer

Determine whether the series is convergent or divergent by expressing $S _ { n }$ as a telescoping sum. If it is convergent, find its sum.
$$\sum _ { n = 2 } ^ { \infty } \frac { 5 } { n \left( n ^ { 2 } - 1 \right) }$$

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Definitions:

Fermentation

A metabolic process that converts sugar to acids, gases, or alcohol in the absence of oxygen.

Gravity

A natural phenomenon by which all things with mass or energy are brought toward one another, including objects ranging from subatomic particles to planets and stars.

Energy

The capacity to do work or produce change, present in many forms such as kinetic, thermal, electrical, and chemical.

Muscle Contractions

The process whereby muscle fibers shorten or lengthen to produce movement or apply force against resistance.