计算(-1)÷2+(-1/2)÷3+(-1/3)÷4+(-1/4)÷5+...+(-1/2010)÷2011

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计算(-1)÷2+(-1/2)÷3+(-1/3)÷4+(-1/4)÷5+...+(-1/2010)÷2011
计算(-1)÷2+(-1/2)÷3+(-1/3)÷4+(-1/4)÷5+...+(-1/2010)÷2011

计算(-1)÷2+(-1/2)÷3+(-1/3)÷4+(-1/4)÷5+...+(-1/2010)÷2011
(-1)÷2+(-1/2)÷3+(-1/3)÷4+(-1/4)÷5+...+(-1/2010)÷2011
=-[1/(1×2)+1/(2×3)+...+1/(2010×2011)]
=-(1-1/2+1/2-1/3+...+1/2010-1/2011)
=-(1-1/2011)
=-2010/2011

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