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AP® Calculus AB-BC

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Moderate

Find A Power Series

APCALC-0ZKU7G

Find a power series for the function $f( x ) =\cfrac{1}{ 2-x } $ centered at $x = 1$.

A

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

B

$\sum _{ n=0 }^{ \infty }{ \cfrac { { ( x-1 ) }^{ n } }{ { 2 }^{ n+1 } } } $

C

$\sum _{ n=0 }^{ \infty }{ \left( \cfrac { x-1 }{ 2 } \right) ^{ n } } $

D

$\sum _{ n=0 }^{ \infty }{ \left( \cfrac { x-1 }{ 3 } \right) ^{ n } } $