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Moderate

# Power Series for Cosine

APCALC-YGI8EK

Which of the following series represents a power series centered at zero for $\cos(2x)$?

A

$x-\dfrac { { x }^{ 3 } }{ 3! } +\dfrac { { x }^{ 5 } }{ 5! } -...+\dfrac { { \left( -1 \right) }^{ n-1 }{ x }^{ 2n-1 } }{ \left( 2n-1 \right) ! } +...$

B

$1-\dfrac { { x }^{ 2 } }{ 2! } +\dfrac { { x }^{ 4 } }{ 4! } -...+\dfrac { { \left( -1 \right) }^{ n-1 }{ x }^{ 2n } }{ \left( 2n \right) ! } +...$

C

$2-\dfrac { { 2x }^{ 2 } }{ 2! } +\dfrac { { 2x }^{ 4 } }{ 4! } -...+\dfrac { { \left( -1 \right) }^{ n-1 }{ 2x }^{ 2n } }{ \left( 2n \right) ! } +...$

D

$1-\dfrac { { \left( 2x \right) }^{ 2 } }{ 2! } +\dfrac { { \left( 2x \right) }^{ 4 } }{ 4! } -...+\dfrac { { \left( -1 \right) }^{ n-1 }{ \left( 2x \right) }^{ 2n } }{ \left( 2n \right) ! } +...$