1/(1*3)=(1/2)*((1/1)-(1/3))
1/(3*5)=(1/2)*((1/3)-(1/5))
1/(5*7)=(1/2)*((1/5)-(1/7))
1/(7*9)=(1/2)*((1/7)-(1/9))
1/(9*11)=(1/2)*((1/9)-(1/11))
1/(11*13)=(1/2)*((1/11)-(1/13))
1/(13*15)=(1/2)*((1/13)-(1/15))
1/(15*17)=(1/2)*((1/15)-(1/17))
.
一直到最后项相加,等於
(1/2)*( (1/1)-(1/3) +(1/3)-(1/5)+(1/5)-(1/7)+.+(1/19)-(1/21))
=(1/2)*((1/1)-(1/21))
= 10/21