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

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

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

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

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2010-1/2011)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011
=1-1/2011
=2010/2011
因为前边的把后面的抵消了

=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010+1/2010-1/2011
=1-1/2011
=2010/2011

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