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