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