1/3=1/(1*3)=1/2(1-1/3)
1/15=1/(3*5)=1/2(1/3-1/5)
.
1/3+1/15+1/35+1/63+1/99=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)=1-1/11=10/11