(-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