1/3+1/8+1/15+...+1/120=1/2*(2/3+1/4+2/15+...+1/60)=1/2*[(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+(1/5-1/7)+(1/6-1/8)+)+(1/7-1/9)+(1/8-1/10))+(1/9-1/11)+(1/10-1/12)=1/2*(1+1/2-1/11-1/12)=1/2*175/132=175/264
