Find the Radius of Convergence and the Interval of Convergence $$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x - 8 ) ^ { n } } { \sqrt { n } }$$

question 96

Multiple Choice

Find the radius of convergence and the interval of convergence of the power series.
$$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( x - 8 ) ^ { n } } { \sqrt { n } }$$

• A) \(R = 1 , l = [ 7,9 )\)
• B) \(R = 1 , I = ( 7,9 ]\)
• C) \(R = 8 , l = [ - 8,8 )\)
• D) \(R = 8 , I = ( - 8,8 )\)

Identify the effects of price changes on consumer behavior and market outcomes.

Comprehend the concept of equilibrium price and how market dynamics strive to achieve it.

Understand the economic decision-making process in both for-profit and not-for-profit organizations.

Acknowledge the relationship between microeconomics decisions and their broader macroeconomic implications.

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Definitions:

Mafic Crystals

Minerals rich in magnesium and iron that crystallize from basaltic magmas, typically dark in color.

Pegmatite

An igneous rock with extremely large crystals, formed by the slow cooling of magma, often containing rare minerals.

Texture

The general physical appearance or character of a rock, especially the size, shape, and arrangement of minerals and other materials.

Viscosity

A measure of a material’s resistance to flow.