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

Essay

Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n } \frac { n } { 4 ^ { n } }$ .(a) Show that the series is absolutely convergent.(b) How many terms of the series do we need to add in order to find the sum to within 0.002?
(c) What is the approximation sum in part (b)?