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Show That the Series ∑n=1∞(−1)n−13n+1\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { 3 n + 1 }

Question 333

Essay

Show that the series ∑n=1∞(−1)n−13n+1\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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