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

question 46

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) \(R = 8 , l = ( - 8,8 )\)

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Definitions:

Fibrocartilage

A type of tough, very dense, white connective tissue with a matrix containing collagen fibers, providing support and shock absorption.

Synchondrosis

A type of joint where bones are joined by hyaline cartilage, allowing very little or no movement between the bones.

Syndesmosis

A fibrous joint at which two bones are bound by long collagen fibers, allowing for minimal movement, typically found between the tibia and fibula.

Inversion

A term that can refer to the process of turning something inside out or upside down, but in genetics, it describes a chromosome rearrangement in which a segment of a chromosome is reversed end to end.