1\2x4+1\4x6+1\6x8+…+1\2012x2014等于?,
问题描述：
1\2x4+1\4x6+1\6x8+…+1\2012x2014等于?,
答
设S=1\2x4+1\4x6+1\6x8+…+1\2012x2014
则4*S=1\1*2+1\2*3+1\3*4+……+1/1006*1007
4*S=1\1-1\2+1\2-1\3+1\3-1\4+……+1\1006-1\1007
4*S=1-1\1007=1006\1007
S=503/2014
答
原式
=1/2x(2/2x4+2/4x6+2/6x8+···+2/2012x2014)
=1/2x(1/2-1/4+1/4-1/6+1/6-1/8+···+1/2012-1/2014)
=1/2x(1/2-1/2014)
=1/2x1006/2014
=1003/2014