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) \(( 0,12 )\)

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Definitions:

Color Vision

The ability of the visual system to distinguish objects based on the wavelengths of the light they reflect, emit, or transmit.

Cones

Photoreceptor cells in the retina of the eye that function best in relatively bright light and enable the perception of color.

Dim Light

A low level of illumination, often creating a subdued or intimate atmosphere.

Cones

Photoreceptor cells in the retina of the eye that are responsible for color vision and function best in relatively bright light.