数学试题讲解

设

f (x) = {\begin{cases} x, 0 \leq x \leq \frac{1}{2} \\ 2 - 2 x, \frac{1}{2} < x < 1 \end{cases}

，

S (x) = \frac{a_{0}}{2} + \sum_{n = 1}^{\infty} a_{n} \cos n π x, - \infty < x < + \infty,

其中

a_{n} = 2 \int_{0}^{1} f (x) \cos n π x d x (n = 0, 1, 2, \dots)

，则

S (- \frac{5}{2})

等于

\frac{1}{2}

- \frac{1}{2}

\frac{3}{4}

- \frac{3}{4}