Determine If the Series $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 n - 1 } { 4 n + 1 } \right) ^ { n }$

question 160

Essay

Determine if the series $\sum _ { n = 1 } ^ { \infty } \left( \frac { 3 n - 1 } { 4 n + 1 } \right) ^ { n }$ converges or diverges by the Ratio Test or Root Test.

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Definitions:

Americanization Programs

Initiatives aimed at assimilating immigrants into American culture, traditionally focusing on teaching English and American history and government.

Lusitania

A British ocean liner sunk by a German submarine in 1915 during World War I, an event that significantly affected public opinion and contributed to the US entering the war.

Race Betterment Foundation

An organization established in the early 20th century advocating for eugenics and the improvement of human genetic traits through selective breeding.

John Harvey Kellogg

An American medical doctor, nutritionist, inventor, health activist, and businessman known for the invention of corn flakes and other health foods.