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

question 37

Short Answer

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

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Definitions:

Cellular Slime Molds

Organisms that live as single cells during one phase of their life cycle but can aggregate to form multicellular reproductive structures when food is scarce.

Belt-like Flagellum

A specialized type of flagellum that encircles a cell, typically found in certain protozoan organisms, aiding in locomotion or feeding.

Dinoflagellates

Single-celled, aquatic protists that move with a whirling motion; may be heterotrophic or photosynthetic.

Euglenoids

Single-celled organisms found in freshwater environments, characterized by their elongated shapes and the presence of a flagellum for movement.