请计算1/1*2+1/2*3+1/3*4+……+1/2010*2011等于多少

问题描述:

请计算1/1*2+1/2*3+1/3*4+……+1/2010*2011等于多少

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)
=1-1/2011
=2010/2011