Determine Whether the Series $\sum _ { n = 1 } ^ { \infty } \frac { n - 1 } { 5 n + 1 }$

question 194

Short Answer

Determine whether the series $\sum _ { n = 1 } ^ { \infty } \frac { n - 1 } { 5 n + 1 }$ is convergent or divergent. If it is convergent, find the sum.

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Definitions:

Fourteenth Amendment

An amendment to the U.S. Constitution, adopted in 1868, that grants citizenship to all persons born or naturalized in the United States, including former slaves, and guarantees all citizens equal protection of the laws.

Pre-Civil War

Pre-Civil War refers to the period in United States history before the start of the American Civil War in 1861, characterized by growing tensions over issues like slavery and states' rights.

Civil Rights Act of 1964

The Civil Rights Act of 1964 is a landmark piece of federal legislation in the United States that prohibited discrimination on the basis of race, color, religion, sex, or national origin, particularly in voting, employment, and public accommodations.

Voting Rights Act of 1965

A landmark piece of federal legislation in the United States that aimed to eliminate racial discrimination in voting.