计算(-1X1/2)+(-1/2X1/3)+(-1/3X1/4)+.+(-1/2009X1/2010)的值了

问题描述:

计算(-1X1/2)+(-1/2X1/3)+(-1/3X1/4)+.+(-1/2009X1/2010)的值了

本题用裂项法,

(-1X1/2)+(-1/2X1/3)+(-1/3X1/4)+.+(-1/2009X1/2010)
=-(1-1/2+1/2-1/3+1/3-1/4+.+1/2009-1/2010)
=-(1-1/2010)
=-2009/2010