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

Multiple Choice

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

A) $a _ { 0 } = - 2 / \pi , b _ { n } = 0 , a _ { n } = 0$
B) $a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi ) , a _ { n } = 0$
C) $a _ { 0 } = 0 , b _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi ) , a _ { n } = 0$
D) $a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n } 2 / ( n \pi )$
E) $a _ { 0 } = 0 , b _ { n } = 0 , a _ { n } = ( - 1 ) ^ { n + 1 } 2 / ( n \pi )$