1/1x2+1/2x3+.1/2010x2011=?
4个回答

1/(1×2)=1-1/2

1/(2×3)=1/2-1/3

1/1x2+1/2x3+1/3x4+…+1/2010x2011

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

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

=1-1/2011

=2010/2011

裂项求和