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

question 203

Essay

Consider the series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n - 1 } \frac { n } { 4 ^ { n } }$ .(a) Show that the series is absolutely convergent.(b) Calculate the sum of the first 3 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).

Explain the significance of primary systems and their influence on parties and the public.

Describe and assess the importance of demographic factors in voting behavior and election outcomes.

Examine the evolution of suffrage rights in the United States and the impact of federal government actions on voting rights expansion.

Discuss the structure and strategy of modern presidential campaigns.

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