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