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=
1/3+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*(1-1/3+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)
=1/2*12/13
=6/13