解
原式=1+1/15+3+1/35+5+1/63+7+1/99+9+1/143+11+1/195
=1+3+5+7+9+(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+(1/13- 1/15)*1/2
=36+(1/3-1/5+1/5-1/7+...+1/13-1/15)*1/2
=36+(1/3-1/15)*1/2
=36又2/15