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AP® Calculus AB-BC

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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

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

B

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

C

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

D

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