Find the Taylor Series for the Given Function at the Indicated

question 14

Multiple Choice

Find the Taylor series for the given function at the indicated point $x = a \text {. }$ $f ( x ) = \ln ( 5 x ) ; a = \frac { 1 } { 5 }$

• A) \(\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 5 ^ { n } } { n } \left( x - \frac { 1 } { 5 } \right) ^ { n }\)
• B) \(\sum _ { n = 1 } ^ { \infty } \frac { 5 ^ { n } } { n } \left( x - \frac { 1 } { 5 } \right) ^ { n }\)
• C) \(\sum _ { n = 1 } ^ { \infty } \frac { 1 } { n 5 ^ { n } } \left( x - \frac { 1 } { 5 } \right) ^ { n }\)
• D) \(\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { n 5 ^ { n } } \left( x - \frac { 1 } { 5 } \right) ^ { n }\)

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