Determine Whether the Series Is Convergent or Divergent $$\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( 7 n ) ! }$$

question 20

Short Answer

Determine whether the series is convergent or divergent. $$\sum _ { n = 1 } ^ { \infty } \frac { ( n ! ) ^ { 4 } } { ( 7 n ) ! }$$

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Definitions:

Carbohydrate Cycle

The series of processes by which carbohydrates are synthesized, broken down, and reused in the biosphere.

Protein Cycle

The dynamic process of protein synthesis, utilization, degradation, and recycling within living organisms.

Phosphorus

A chemical element with the symbol P, essential for life, found in DNA, RNA, ATP, and phospholipids.

Sulphur Dioxide

A colorless gas with a sharp, choking smell, produced by volcanic activity or burning fossil fuels, and is a significant air pollutant.