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

question 187

Essay

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).

Understand the concept and roles of fiscal policy in an economy.

Identify the goals of government programs and the nature of government transfer programs.

Explain the concept of externalities and their impact on society.

Recognize the main and secondary sources of revenue for the U.S. federal government.

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Definitions:

Ordinal Data

Data that can be categorized and ranked; however, the intervals between the categories are not necessarily equal.

Nominal Variable

A categorical variable for which different values represent different categories without any intrinsic ranking order.

Interval Data

A type of numerical data involving measurements where both the order and the exact differences between the measurements matter, but there is no true zero point.

Quantitative Data

Data that can be quantified and verified, and is amenable to statistical manipulation. It represents the quantity of something rather than its quality.