Determine If the Series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 6 ^ { n } n ! }$

question 288

Essay

Determine if the series $\sum _ { n = 1 } ^ { \infty } \frac { 2 \cdot 5 \cdot 8 \cdot \ldots \cdot ( 3 n - 1 ) } { 6 ^ { n } n ! }$ converges or diverges by the Ratio Test or Root Test.

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Definitions:

Gene Replication

The biological process by which a cell copies its DNA prior to cell division, ensuring that each new cell receives a full set of genetic information.

Gene Replication

The process by which a cell makes an exact copy of its genes during cell division.

Mutation

A change in the DNA sequence that can lead to alterations in gene function or expression, potentially causing variations in physical traits or health conditions.

Epigenetic Mark

Chemical modifications to DNA or histones that change gene activity without altering the DNA sequence, affecting how cells read genes.