The Fourier Series of the Function $f ( x ) = x$

question 35

Multiple Choice

The Fourier series of the function $f ( x ) = x$ on $[ - 1,1 ]$ is

• A) \(\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } 2 \cos ( n \pi x ) / ( n \pi )\)
• B) \(\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 \cos ( n \pi x ) / ( n \pi )\)
• C) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n } 2 \sin ( n \pi x ) / ( n \pi )\)
• D) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } 2 \sin ( n \pi x ) / ( n \pi )\)
• E) \(\sum _ { n - 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } \sin ( n \pi x ) / ( n \pi )\)

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