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).

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Definitions:

Secondary Market

Sales of existing securities between investors. Compare with Primary market.

Stock

An ownership share in a corporation, representing a claim on part of the company's assets and earnings.

Transaction

An instance of buying or selling something; a business deal or financial arrangement between two parties.

Short-Term Debt Securities

Financial instruments that represent borrowed money which must be repaid within a short period, typically less than one year.