1/3+1/15+1/35+1/63+1/99+1/143+1/195简便

1/3=1/2(1-1/3)
1/15=1/2(1/3-1/5)
1/35=1/2(1/5-1/7)
1/63=1/2(1/7-1/9)
.
.
1/195=1/2(1/13-1/15)
1/3+1/15+1/35+1/63+1/99+1/143+1/195
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...-1/13+1/13-1/15)
=1/2(1-1/15)
=1/2*14/15
=7/15