1/1*3+1/3*5+1/5*7+.1/17*19+1/19*21的公式

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=（1-1/3）*(1/2)+(1/3-1/5)*(1/2)+(1/5-1/7)*(1/2)+......+(1/17-1/19)*(1/2)+(1/19-1/21)*(1/2)
=(1-1/3+1/3-1/5+1/5-1/7+......+1/17-1/19+1/19-1/21)*(1/2)
=(1-1/21)*(1/2)
=(20/21)*(1/2)
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21=1/2(1-1/3+1/3-1/5+1/5-1/7+......+1/17-1/19+1/19-1/21)=1/2(1-1/21)=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+....+(1/17-1/19)+(1/19-1/21)]/2
=[1-1/21]/2
=10/21

1/1*3+1/3*5+1/5*7+....1/17*19+1/19*21
=1/2*(1-1/3+1/3-1/5+1/5-.................-1/19+1/19-1/21)
=1/2*(1-1/21)
=10/21

=(1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19+1/19-1/21)/2
=(1-1/21)/2
=(20/21)/2
=10/21