Consider the Series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 1 } { ( 4 n ) ! }$

question 21

Essay

Consider the series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 1 } { ( 4 n ) ! }$ .(a) Show that $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 1 } { ( 4 n ) ! }$ is absolutely convergent.(b) Calculate the sum of the first 3 terms to approximate the sum of the series.(c) Estimate the error involved in the approximation from part (b).

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