1/3*7+1/7*11+1/11*15+...+1/25*39=1/4*(1/3-1/7)+1/4*(1/7-1/11)+1/4*(1/11-1/15)+...+1/4*(1/25-1/29)=1/4*(1/3-1/7+1/7-1/11+1/11-1/15+...+1/25-1/29)=1/4*(1/3-1/29)=1/4*26/87=13/174