一題高中學的函數的題目?

原式 = f(1/1006) + f(2/1006) + f(3/1006) + ... + f(1006/1006) + ... + f(2012/1006)
利用提示分組相加:
= f(1/1006)+f(1005/1006) + f(2/1006)+f(1004/1006) + ... + f(502/1006)+f(504/1006)
= 1 × 502
+ f(503/1006) = 0.5
+ f(1006/1006) = 0
+ f(1007/1006)+f(2011/1006) + f(1008/1006)+f(2010/1006) + ... + f(1508/1006)+
f(1510/1006) = 1 × 502
+ f(1509/1006) = 0.5
+ f(2012/1006) = 0

答案是 502 + 0.5 + 0 + 502 + 0.5 + 0 = 1005。