Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n } { n ^ { 2 } + 1 }$ .(a) Show that the series is convergent, but not absolutely convergent.(b) Calculate the sum of the first 8 terms to approximate the sum of the series.(c) Is the approximation in part (b) an overestimate or an underestimate?
(d) Estimate the error involved in the approximation from part (b).

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The Answer of Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n } { n ^ { 2 } + 1 }$ .(a) Show that the series is convergent, but not absolutely convergent.(b) Calculate the sum of the first 8 terms to approximate the sum of the series.(c) Is the approximation in part (b) an overestimate or an underestimate?
(d) Estimate the error involved in the approximation from part (b).

Consider the Series ∑n=1∞(−1)n−1nn2+1\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n } { n ^ { 2 } + 1 }∑n=1∞​(−1)n−1n2+1n​

Consider the Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n } { n ^ { 2 } + 1 }$