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AP® Calculus AB-BC

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Moderate

Power Series Substitution

APCALC-XKZKON

Find the power series for $f( x ) = \cfrac{1}{{ x }^{ 2 }+1 } $ centered at $x = 0$.

A

$\sum _{ n=0 }^{ \infty }{ { x }^{ 2n\qquad } } $

B

$\sum _{ n=0 }^{ \infty }{ { -x }^{ 2n\qquad } } $

C

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

D

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