1/1x3+1/2x4+1/3x5+…+1/2011x2013+1/2012x2014=多少
问题描述：
1/1x3+1/2x4+1/3x5+…+1/2011x2013+1/2012x2014=多少
答
裂项法：1/1x3+1/2x4+1/3x5+…+1/2011x2013+1/2012x2014=1/2×（1-1/3+1/2-1/4+1/3-1/5+……+1/2011-1/2013+1/2012-1/2014）=1/2×（1+1/2-1/2013-1/2014）=1/2×6077246/4054182=3038623/4054182