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Find a Power Series Representation For f(t)=ln(14t)f ( t ) = \ln ( 14 - t )

Question 26

Multiple Choice

Find a power series representation for f(t) =ln(14t) f ( t ) = \ln ( 14 - t )


A) ln14n=1tn14n\ln 14 - \sum _ { n = 1 } ^ { \infty } \frac { t ^ { n } } { 14 ^ { n } }
B) ln14n=1tnn14n\ln 14 - \sum _ { n = 1 } ^ { \infty } \frac { t ^ { n } } { n 14 ^ { n } }
C) n=0tnn14n\sum _ { n = 0 } ^ { \infty } \frac { t ^ { n } } { n 14 ^ { n } }
D) n=114tnnn\sum _ { n = 1 } ^ { \infty } \frac { 14 t ^ { n } } { n ^ { n } }
E) ln14+n=1t2n14n\ln 14 + \sum _ { n = 1 } ^ { \infty } \frac { t ^ { 2 n } } { 14 ^ { n } }

Correct Answer:

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