2001.817
1/2+2/3+3/4+...+2009/2010
=(1-1/2)+(1-1/3)+(1-1/4)+...+(1-1/2010)
=2009-(1/2+1/3+1/4+……+1/2009+1/2010)
关于1/2+1/3+1/4+……+1/2009+1/2010的求法,具体可参考:
1/2+1/3+1/4+……+1/2009+1/2010
=ln(2010)+C-1
≈7.60589+0.57722-1
=7.18311
(C是欧拉常数≈0.57722)
∴原式
=2009-7.183
=2001.817