Differentiate the Series For $- \frac { 1 } { x }$

question 61

Multiple Choice

Differentiate the series for $- \frac { 1 } { x }$ to find the power series for the function $f ( x ) = \frac { 6 } { x ^ { 2 } }$ .

• A) \(6 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ( x - 1 ) ^ { n - 1 }\)
• B) \(\sum _ { n = 1 } ^ { \infty } ( - 6 ) ^ { n } n ( x - 1 ) ^ { n - 1 }\)
• C) \(6 \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ( x - 1 ) ^ { n - 1 }\)
• D) \(\sum _ { n = 0 } ^ { \infty } ( - 6 ) ^ { n - 1 } n ( x - 1 ) ^ { n }\)
• E) \(\sum _ { n = 0 } ^ { \infty } ( - 6 ) ^ { n - 1 } n ( x - 1 ) ^ { n + 1 }\)

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