Show That the Series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { 4 n }$

question 295

Essay

Show that the series $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { 4 n }$ 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:

Syntactically Anomalous Words

Words or phrases that deviate from the expected grammatical structure within a sentence, often used in studies of language processing and comprehension.

Propositional Complexity

The number of underlying distinct ideas in a sentence.

Antecedent Information

Background or prior information that helps to explain or contextualize an event, situation, or behavior.

Clause

A grammatical unit that contains both a subject and a predicate.