解：1/(1+2)+1/(1+2+3)+1/(1+2+3+4）+。。。+1/(1+2+3+4...+2013) =2/(2×3)+2/(3×4)+2/(4×5)+...+2/(2013×2014) =2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/2013-1/2014) =2(1/2-1/2014) =1006/1007
