Show That the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { 3 n + 1 }$

question 333

Essay

Show that the series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { 3 n + 1 }$ is convergent. How many terms of the series do we need to add to find the sum to within 0.01?

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Definitions:

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Organizations formed by workers to protect their collective interests, rights, and working conditions.

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Compromises made by one party in negotiations, typically involving relinquishing certain demands to reach an agreement.

Rank And File

The ordinary members of an organization, especially a union, as compared to its leadership.

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Individuals who have joined a union to benefit from collective bargaining and other protections and support the union provides.