Determine If the Series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 2 ^ { n } n ! }$

question 85

Essay

Determine if the series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 2 ^ { n } n ! }$ converges or diverges by the Ratio Test or Root Test.

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Definitions:

Immune Systems

The complex network of cells, tissues, and organs that work together to defend the body against infections, diseases, and foreign substances.

Transductive Reasoning

A type of reasoning in which specific cases are used to form a general conclusion, often seen in early childhood cognitive development.

Inductive

A systematic approach where multiple assertions, believed or generally accepted as true, are amalgamated to arrive at a targeted conclusion.

Deductive

A logical process where a conclusion follows necessarily from the stated premises, moving from general principles to specific instances.