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

question 30

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

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Definitions:

GnRH

Gonadotropin-releasing hormone, a hormone responsible for the release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) from the anterior pituitary gland.

TSH

Thyroid-Stimulating Hormone, a pituitary gland secreted hormone that regulates the production of hormones by the thyroid gland.

Thyroid Hormones

Hormones produced by the thyroid gland, such as thyroxine (T4) and triiodothyronine (T3), that regulate metabolism, energy generation, and growth.

Follicular Cells

Epithelial cells found in the thyroid gland which synthesize and secrete thyroid hormones, or cells surrounding the ovum in an ovarian follicle.