Find a Geometric Power Series for the Function Centered at 0

question 4

Multiple Choice

Find a geometric power series for the function centered at 0, (i) by the technique shown in Examples 1 and 2 and (ii) by long division. $$f ( x ) = \frac { 10 } { 4 - x }$$

• A)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 5 } { 2 } \left( \frac { x } { 4 } \right) ^ { n } , | x | < 4\)
• B)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 1 } { 4 } \left( \frac { x } { 4 } \right) ^ { n } , | x | < 4\)
• C)
• \(\sum _ { n = 0 } ^ { \infty } 10 \left( - \frac { x } { 4 } \right) ^ { n } , | x | < 4\)
• D)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 5 } { 2 } ( - 4 x ) ^ { n } , | x | < 4\)
• E)
• \(\sum _ { n = 0 } ^ { \infty } \frac { 5 } { 2 } ( - x ) ^ { n } , | x | < 1\)

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Definitions:

Median

The middle value in a data set, which separates the higher half from the lower half when the numbers are arranged in order.

Mode

Most frequently occurring score or value of a variable in a set of data.

Range

The difference between the highest and lowest values in a data set, indicating the span of data points.

Standard Deviation

A measure of the dispersion or variability within a set of numerical data, indicating how spread out the values are from the mean.