Find the Interval of Convergence of the Power Series $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 12 ) ^ { n - 1 } } { 12 ^ { n - 1 } }$

question 16

Multiple Choice

Find the interval of convergence of the power series $\sum _ { n = 0 } ^ { \infty } \frac { ( x - 12 ) ^ { n - 1 } } { 12 ^ { n - 1 } }$ .
(Be sure to include a check for convergence at the endpoints of the interval.)

• A) \(( - \infty , 0 ) \cup ( 24 , \infty )\)
• B) \(( - \infty , 0 ] \cup [ 12 , \infty )\)
• C) \([ 0,24 ]\)
• D) \(( 0,24 )\)
• E) \(( 0,12 )\)

---

Definitions:

Supreme Court

The highest judicial court in the United States, with ultimate appellate jurisdiction over all federal and state court cases that involve a point of federal law.

Liberty League

An organization or group advocating for individual freedoms and rights, historically or contemporarily.

New Deal Program

A series of programs, public work projects, financial reforms, and regulations enacted by President Franklin D. Roosevelt in the United States during the 1930s to address the Great Depression.