问题
填空题
设f(x)=
|
答案
∵f(x)=
，4x 4x+2
∴f（x）+f（1-x）=
+4x 4x+2 41-x 41-x+2
=
+4x 4x+2 41-x•4x (41-x+2)•4x
=
+4x 4x+2
=4 4+2•4x
+4x 4x+2 2 2+4x
=
=14x+2 4x+2
故可得f(
)+f(1 2015
)+f(2 2015
)+…f(3 2015
)2014 2015
=f(
)+f(1 2015
)+f(2014 2015
)+f(2 2015
)+…+f(2013 2015
)+f(1002 2015
)1003 2015
=1007×1=1007