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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