1/3+1/15+1/35+1/63+1/99+1/143=?

1/3+1/15+1/35+1/63+1/99+1/143=?
1/3+1/15+1/35+1/63+1/99+1/143=?

1/3+1/15+1/35+1/63+1/99+1/143=?
=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13
=(1/2)(1-1/3)+(1/2)(1/3-1/5)+(1/2)(1/5-1/7)+(1/2)(1/7-1/9)+(1/2)(1/9-1/11)+(1/2)(1/11-1/13)
=(1/2)(1-1/13)
=6/13

1/3=(1-1/3)/2
1/15=(1/3-1/5)/2
1/35=(1/5-1/7)/2
1/63=(1/7-1/9)/2
...1/143=(1/11-1/13)/2
所以原式=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+...+(1/11-1/13)/2
=(1-1/13)/2
=6/13