这道题简便算法怎么做！！！！谢谢！

2/15+2/35+2/63+2/99+2/143
=(1/3-1/5)+(1/5-1/7)+(1/7+1/9)+(1/9-1/11)+(1/11-1/13)
=1/3-1/5+1/5-1/7+1/7+1/9+1/9-1/11+1/11-1/13
=1/3-1/13
=10/39

1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)
=1-(1/2+1/3)+(1/3+1/4)-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)+(1/9+1/10)
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9+1/9+1/10
=1-1/2+1/10
=3/5

2/15+2/35+2/63+2/99+2/143

=2/(3*5)+2/(5*7)+2/(7*9)+2/(9*11)+2/(11*13)

=(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)

=1/3-1/13

=10/39

1-(5/6)+(7/12)-(9/20)+(11/30)-(13/42)+(15/56)-(17/72)+(19/90)

=[1-(5/6)]+[(7/12)-(9/20)]+[(11/30)-(13/42)]+[(15/56)-(17/72)]+(19/90)

=1/6+8/60+12/210+(15/7-15/8-17/8+17/9)+19/90

=1/6+2/15+2/35+2/63+19/90

=1/2-1/3+1/3-1/5+1/5-1/7+1/7-1/9+19/90

=1/2+19/90

=64/90

=32/45