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AP® Calculus AB-BC

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Moderate

Taylor Series For $\ln x$

APCALC-J4JGZH

Find the Taylor series for $f( x ) =\ln { x } $ centered at $x = 1$.

A

$\sum _{ n=0 }^{ \infty }{ \cfrac { { ( -1 ) }^{ n+1 }{ ( x-1 ) }^{ n+1 } }{ n+1 } } $

B

$\sum _{ n=0 }^{ \infty }{ \cfrac { { ( -1 ) }^{ n }{ ( x-1 ) }^{ n+1 } }{ n+1 } } $

C

$\sum _{ n=0 }^{ \infty }{ \cfrac { { ( -1 ) }^{ n }{ ( x-1 ) }^{ n+1 } }{ ( n+1 ) ! } } $

D

$\sum _{ n=0 }^{ \infty }{ \cfrac { { ( -1 ) }^{ n+1 }{ ( x-1 ) }^{ n } }{ n! } } $