1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21

1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15+1/15*17+1/17*19+1/19*21
=(2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15+2/15*17+2/17*19+2/19*21)*1/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15+1/15-1/17+1/17-1/19+1/19-1/21)*1/2
=(1-1/21)*1/2
=20/21*1/2
=10/21

1/2*[(1-1/3)+(1/3-1/5)+......(1/19-1/21)]
=1/2(1-1/21)
=10/21

1/2*[(1-1/3)+(1/3-1/5)+......(1/19-1/20)]
=1/2(1-1/20)
=19/40

1