1x3 / 1 + 3x5 / 1 + 5x7 / 1 + 7x9 / 1 + ····· + 19x21 / 1 = write the calculation process

1x3 / 1 + 3x5 / 1 + 5x7 / 1 + 7x9 / 1 + ····· + 19x21 / 1 = write the calculation process

1/1×3+1/3×5+1/5×7+1/7×9+...+1/19×+21
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+...+(1/19-1/21)/2
=(1-1/3+1/3-1/5+1/5-1/7+...+1/19-1/21)/2
=(1-1/21)/2
=10/21

1 / 1x3 = 1 / 2x (1x1 / 3), 1 / 3x5 = 1 / 2x (1 / 3-1 / 5), 1 / 5x7 = 1 / 2x (1 / 5x1 / 7)... Calculate 1 / 1x3 + 1 / 3x5 + 1 / 5x7.. + 1 / 2009x2011 =?

1/1x3+1/3x5+1/5x7..+1/2009x2011
=1/2x[(1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/2009-1/2011)]
=1/2x(1-1/2011)
=1/2x2010/2011
=1005/2011